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A153140 Coefficients of the second order mock theta function B(q). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A218004 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

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Last modified July 4 15:25 EDT 2020. Contains 335448 sequences. (Running on oeis4.)