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A136569 McKay-Thompson series of class 19A for the Monster group with a(0) = 3. 3
1, 3, 6, 10, 21, 36, 61, 96, 156, 232, 357, 522, 768, 1092, 1563, 2174, 3039, 4164, 5695, 7686, 10362, 13792, 18333, 24138, 31706, 41316, 53712, 69348, 89319, 114396, 146114, 185724, 235482, 297252, 374316, 469578, 587646, 732888, 911961, 1131250 (list; graph; refs; listen; history; text; internal format)
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)

Index entries for McKay-Thompson series for Monster simple group

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-Fran├žois 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

Cf. A058549(n) = a(n) unless n=0.

Sequence in context: A068882 A076713 A299017 * A061883 A027671 A167617

Adjacent sequences:  A136566 A136567 A136568 * A136570 A136571 A136572

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 07 2008

STATUS

approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)