A053269 - OEIS

A053269

Coefficients of the '6th-order' mock theta function psi(q).

0, 1, -1, 1, -2, 3, -2, 2, -4, 5, -5, 5, -7, 9, -8, 9, -12, 14, -15, 16, -20, 23, -23, 25, -31, 36, -37, 40, -47, 54, -56, 60, -71, 79, -84, 91, -103, 115, -121, 131, -149, 164, -174, 188, -210, 232, -245, 264, -294, 321, -343, 368, -406, 443, -470, 505, -554, 602, -641, 687, -751, 813, -863, 925 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,5`
	REFERENCES	`Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 4, 13`
	LINKS	`Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from G. C. Greubel)` `George E. Andrews and Dean Hickerson, Ramanujan's "lost" notebook VII: The sixth order mock theta functions, Advances in Mathematics, 89 (1991) 60-105.`
	FORMULA	`G.f.: psi(q) = Sum_{n >= 0} (-1)^n q^(n+1)^2 (1-q)(1-q^3)...(1-q^(2n-1)) /((1+q)(1+q^2)...(1+q^(2n+1))).` `a(3n + 1) = A262614(n). a(3n + 2) = - A263041(n). - Michael Somos, Apr 17 2016` `a(n) ~ -(-1)^n * exp(Pisqrt(n/6)) / (2sqrt(3*n)). - Vaclav Kotesovec, Jun 15 2019`
	MATHEMATICA	`Series[Sum[(-1)^n q^(n+1)^2 Product[1-q^k, {k, 1, 2n-1, 2}]/Product[1+ q^k, {k, 1, 2n+1}], {n, 0, 9}], {q, 0, 100}]` `nmax = 100; CoefficientList[Series[Sum[(-1)^k * x^((k+1)^2) * Product[1-x^j, {j, 1, 2k-1, 2}]/Product[1+ x^j, {j, 1, 2k+1}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 15 2019 *)`
	CROSSREFS	`Other '6th-order' mock theta functions are at A053268, A053270, A053271, A053272, A053273, A053274.` `Cf. A262614, A263041.` `Sequence in context: A194020 A372053 A372048 * A163873 A309563 A292588` `Adjacent sequences: A053266 A053267 A053268 * A053270 A053271 A053272`
	KEYWORD	`sign,easy`
	AUTHOR	`Dean Hickerson, Dec 19 1999`
	STATUS	`approved`