OFFSET
-1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = -1..10000
K. Bringmann and H. Swisher, On a conjecture of Koike on identities between Thompson series and Roger-Ramanujan functions, Proc. Amer. Math. Soc. 135 (2007), 2317-2326. See page 2325 (A.5)
FORMULA
G.f.: x^(-1) * ( G(x) * G(x^19) + x^4 * H(x) * H(x^19) )^3 where G() is g.f. of A003114 and H() is g.f. of A003106.
a(n) ~ exp(4*Pi*sqrt(n/19)) / (sqrt(2)*19^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 07 2017
EXAMPLE
1/q + 3 + 6*q + 10*q^2 + 21*q^3 + 36*q^4 + 61*q^5 + 96*q^6 + 156*q^7 + ...
MATHEMATICA
QP = QPochhammer; G[x_] := 1/(QP[x, x^5]*QP[x^4, x^5]); H[x_] := 1/(QP[x^2, x^5]*QP[x^3, x^5]); s = (G[x]*G[x^19] + x^4*H[x]*H[x^19])^3 + O[x]^40; CoefficientList[s, x] (* Jean-François Alcover, Nov 15 2015 *)
PROG
(PARI) {a(n) = local(A, A1, A2); if( n<-1, 0, n = 2*n + 2 ; A = x^3 * O(x^n) ; A1 = ( eta(x + A) * eta(x^19 + A) / eta(x^2 + A) / eta(x^38 + A) )^2; A2 = -subst(A1, x, -x); A = ( x^4 / A1 / A2 - (A1 + A2) / 4 / x )^3; polcoeff( A, n ))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jan 07 2008
STATUS
approved