A153140 Coefficients of the second order mock theta function B(q).

1, 2, 4, 6, 9, 14, 20, 28, 40, 54, 72, 98, 129, 168, 220, 282, 360, 460, 580, 728, 912, 1134, 1404, 1734, 2129, 2604, 3180, 3864, 4680, 5658, 6812, 8182, 9808, 11718, 13968, 16618, 19720, 23350, 27600, 32550, 38313

Offset: 0

Author

Jeremy Lovejoy, Dec 19 2008

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
• R. J. McIntosh, Second order mock theta functions, Canad. Math. Bull. 50 (2007), 284-290.

Crossrefs

Other '2nd order' mock theta functions are at A006304, A006306.

Programs

Mathematica

nmax = 100; CoefficientList[Series[Sum[x^(k^2+k) * Product[(1+x^(2*j))/(1-x^(2*j+1))^2, {j, 0, k}], {k, 0, Floor[Sqrt[nmax]]}]/2, {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 12 2019 *)

PARI

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

Formula

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

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

a(n) ~ exp(Pi*sqrt(n/2)) / (2^(5/2) * sqrt(n)). - Vaclav Kotesovec, Jun 12 2019

Extensions

More terms from Michel Marcus, Jun 18 2013