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#28byAlois P. Heinz at Tue Feb 02 21:58:47 EST 2021
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#27byJon E. Schoenfield at Tue Feb 02 20:40:19 EST 2021
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#26byJon E. Schoenfield at Tue Feb 02 20:40:17 EST 2021
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| NAME
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Coefficients of the '5th -order' mock theta function phi_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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 19, 22, 23, 25.
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| FORMULA
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G.f.: phi_0(q) = sum for Sum_{n >= >=0 of } q^n^2 (1+q)(1+q^3)...(1+q^(2n-1)).
a(n) = ) is the number of partitions of n into odd parts such that each occurs at most twice and if k occurs as a part then all smaller positive odd numbers occur.
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| CROSSREFS
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Other '5th -order' mock theta functions are at A053256, A053257, A053259, A053260, A053261, A053262, A053263, A053264, A053265, A053266, A053267.
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| STATUS
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approved
editing
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#25byVaclav Kotesovec at Wed Jun 12 03:11:28 EDT 2019
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#24byVaclav Kotesovec at Wed Jun 12 03:11:19 EDT 2019
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| FORMULA
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a(n) ~ sqrt(phi) * exp(Pi*sqrt(n/30)) / (2*5^(1/4)*sqrt(n)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jun 12 2019
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| STATUS
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approved
editing
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#23byOEIS Server at Tue Jun 11 17:29:21 EDT 2019
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| LINKS
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Vaclav Kotesovec, <a href="/A053258/b053258_2.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from G. C. Greubel)
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#22byVaclav Kotesovec at Tue Jun 11 17:29:21 EDT 2019
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Discussion
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| Tue Jun 11
| 17:29
| OEIS Server: Installed new b-file as b053258.txt. Old b-file is now b053258_2.txt.
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#21byVaclav Kotesovec at Tue Jun 11 13:15:10 EDT 2019
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| LINKS
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G. C. GreubelVaclav Kotesovec, <a href="/A053258/b053258_2.txt">Table of n, a(n) for n = 0..100010000</a>> (terms 0..1000 from G. C. Greubel)
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#20byVaclav Kotesovec at Tue Jun 11 13:10:54 EDT 2019
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| MATHEMATICA
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nmax = 100; CoefficientList[Series[Sum[x^(k^2)*Product[1+x^(2*j-1), {j, 1, k}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 11 2019 *)
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| STATUS
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approved
editing
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#19byOEIS Server at Tue Apr 03 08:12:50 EDT 2018
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| LINKS
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G. C. Greubel, <a href="/A053258/b053258_1.txt">Table of n, a(n) for n = 0..1000</a>
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