A153156 Coefficients of the eighth-order mock theta function T_1(q).

1, -1, 2, -2, 3, -4, 5, -6, 8, -9, 11, -14, 17, -20, 24, -28, 33, -39, 46, -53, 62, -72, 83, -96, 110, -126, 145, -165, 188, -214, 243, -275, 312, -352, 396, -447, 502, -563, 632, -707, 791, -884, 986, -1098, 1223, -1359, 1509, -1676, 1857, -2056, 2276, -2515

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

B. Gordon and R. J. McIntosh, Some eighth order mock theta functions, J. London Math. Soc. 62 (2000), 321-335.

Formula

G.f.: Sum{n >= 0} q^(n^2+n) (1+q^2)(1+q^4)...(1+q^(2n))/(1+q)(1+q^3)...(1+q^(2n+1)).

a(n) ~ (-1)^n * sqrt(1 + sqrt(2)) * exp(Pi*sqrt(n)/2) / (2^(11/4) * sqrt(n)). - Vaclav Kotesovec, Jun 14 2019

Mathematica

nmax = 100; CoefficientList[Series[Sum[x^(k*(k+1)) * Product[(1 + x^(2*j)), {j, 1, k}] / Product[(1 + x^(2*j+1)), {j, 0, k}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 13 2019 *)

Prog

(PARI) lista(nn) = my(q = qq + O(qq^nn)); gf = sum(n = 0, nn, q^(n^2+n) * prod(k = 1, n, 1 + q^(2*k)) / prod(k = 0, n, 1 + q^(2*k+1))); Vec(gf) \\ Michel Marcus, Jun 18 2013

Crossrefs

Other '8th-order' mock theta functions are at A153148, A153149, A153155, A153172, A153174, A153176, A153178.

Sequence in context: A137793 A067659 A261772 * A017852 A340751 A319069

Adjacent sequences: A153153 A153154 A153155 * A153157 A153158 A153159

Keyword

sign

Author

Jeremy Lovejoy, Dec 19 2008

Extensions

More terms from Michel Marcus, Feb 23 2015

Status

approved