A288630 McKay-Thompson series of class 6A for the Monster group with a(0) = 10.

1, 10, 79, 352, 1431, 4160, 13015, 31968, 81162, 183680, 412857, 864320, 1805030, 3564864, 7000753, 13243392, 24805035, 45168896, 81544240, 143832672, 251550676, 432030080, 735553575, 1233715328, 2052941733, 3372465024, 5499116975, 8869747264, 14205516345

Offset

-1,2

Links

G. C. Greubel, Table of n, a(n) for n = -1..2500

Formula

G.f. is a period 1 Fourier series which satisfies f(-1 / (6 t)) = f(t) where q = exp(2 Pi i t).

a(n) = A007254(n) = A045484(n) unless n=0.

Convolution square of A058490.

a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(3/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2017

Expansion of A/q - 2 + q/A, where A = (eta(q^2)*eta(q^3)/(eta(q)*eta(q^6) ))^12, in powers of q. - G. C. Greubel, Jun 20 2018

Example

G.f. = x^-1 + 10 + 79*x + 352*x^2 + 1431*x^3 + 4160*x^4 + 13015*x^5 + ...

Mathematica

a[ n_] := With[{A = (QPochhammer[ x^2] QPochhammer[ x^3] / (QPochhammer[ x] QPochhammer[ x^6]))^12}, SeriesCoefficient[ A/x - 2 + x/A, {x, 0, n}]];

Prog

(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); A = (eta(x^2 + A) * eta(x^3 + A) / (eta(x + A) * eta(x^6 + A)))^12; polcoeff( A - 2*x + x^2/A, n))};
(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); A = (eta(x + A) * eta(x^2 + A) / (eta(x^3 + A) * eta(x^6 + A)))^4; polcoeff( A + 14*x + 81*x^2/A, n))};

Crossrefs

Cf. A007254, A045484, A058490.

Sequence in context: A283658 A160655 A006469 * A081905 A016138 A006329

Adjacent sequences: A288627 A288628 A288629 * A288631 A288632 A288633

Keyword

nonn

Author

Michael Somos, Jun 12 2017

Status

approved