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#34byAlois P. Heinz at Tue Feb 02 21:11:08 EST 2021
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#33byJon E. Schoenfield at Tue Feb 02 20:35:35 EST 2021
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#32byJon E. Schoenfield at Tue Feb 02 20:35:31 EST 2021
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| NAME
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Coefficients of the 5th -order mock theta function chi_0(q).
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| REFERENCES
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Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354-355.
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 20, 23, 25.
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| FORMULA
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G.f.: chi_0(q) = sum for Sum_{n >= >=0 of } q^n/((1-q^(n+1))(1-q^(n+2))...(1-q^(2n)))))).
G.f.: chi_0(q) = 1 + sum for Sum_{n >= >=0 of } q^(2n+1)/((1-q^(n+1))(1-q^(n+2))...(1-q^(2n+1)))))).
a(n) = ) is the number of partitions of 5n with rank == 1 (mod 5) minus number with rank == 0 (mod 5)).
a(n) = ) is the number of partitions of n with unique smallest part and all other parts <= twice the smallest part.
a(n) = ) is the number of partitions where the largest part is odd and all other parts are greater than half of the largest part. - N. Sato, Jan 21 2010
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| CROSSREFS
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Other '5th -order' mock theta functions are at A053256, A053257, A053258, A053259, A053260, A053261, A053263, A053264, A053265, A053266, A053267.
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| STATUS
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approved
editing
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#31byOEIS Server at Wed Jun 12 05:14:23 EDT 2019
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| LINKS
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Vaclav Kotesovec, <a href="/A053262/b053262_1.txt">Table of n, a(n) for n = 0..10000</a> (corrected and extended previous b-file from G. C. Greubel)
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#30byBruno Berselli at Wed Jun 12 05:14:23 EDT 2019
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Discussion
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| Wed Jun 12
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| OEIS Server: Installed new b-file as b053262.txt. Old b-file is now b053262_1.txt.
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#29byVaclav Kotesovec at Wed Jun 12 04:37:15 EDT 2019
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#28byVaclav Kotesovec at Wed Jun 12 04:37:08 EDT 2019
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| NAME
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Coefficients of the 5th order mock theta function chi_0(q)).
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| STATUS
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proposed
editing
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#27byVaclav Kotesovec at Wed Jun 12 04:32:17 EDT 2019
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#26byVaclav Kotesovec at Wed Jun 12 04:32:09 EDT 2019
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| FORMULA
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a(n) = number of partitions where the largest part is odd and all other parts are greater than half of the largest part [From _. - _N. Sato_, Jan 21 2010]
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#25byVaclav Kotesovec at Wed Jun 12 04:31:36 EDT 2019
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| FORMULA
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a(n) ~ exp(Pi*sqrt(2*n/15)) / sqrt((5 + sqrt(5))*n). - Vaclav Kotesovec, Jun 12 2019
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| STATUS
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proposed
editing
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