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

0,2

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.

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A346634 A034748 A069916 * A295341 A139135 A097197

Adjacent sequences: A153137 A153138 A153139 * A153141 A153142 A153143

Keyword

nonn

Author

Jeremy Lovejoy, Dec 19 2008

Extensions

More terms from Michel Marcus, Jun 18 2013

Status

approved