A106248 McKay-Thompson series of class 5B for the Monster group with a(0) = -6.

1, -6, 9, 10, -30, 6, -25, 96, 60, -250, 45, -150, 544, 360, -1230, 184, -675, 2310, 1410, -4830, 750, -2450, 8196, 4920, -16180, 2376, -7875, 25644, 15000, -48720, 7126, -22800, 73221, 42310, -134760, 19284, -61400, 194334, 110610, -349000, 49563, -155250, 486370

Offset

-1,2

Links

Seiichi Manyama, Table of n, a(n) for n = -1..10000

Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction

Formula

Expansion of (eta(q) / eta(q^5))^6 in powers of q.

G.f. A(x) satisfies: 0 = f(A(x), A(x^2)) where f(u, v) = u*v * (u*v + 125) - (u+v) * (u^2 - 13 * u*v + v^2).

a(n) = A007252(n) = A045483(n) unless n=0.

Convolution inverse of A121591.

a(n) = A229793(n) - A078905(n) for n > 0. - Seiichi Manyama, Jan 01 2017

a(-1) = 1, a(n) = -(6/(n+1))*Sum_{k=1..n+1} A116073(k)*a(n-k) for n > -1. - Seiichi Manyama, Mar 29 2017

Example

G.f. = 1/q - 6 + 9*q + 10*q^2 - 30*q^3 + 6*q^4 - 25*q^5 + 96*q^6 + 60*q^7 + ...

Mathematica

a[ n_] := SeriesCoefficient[ 1/q (QPochhammer[ q] / QPochhammer[ q^5])^6, {q, 0, n}]; (* Michael Somos, May 22 2013 *)

Prog

(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x + A) / eta(x^5 + A))^6, n))};
(PARI) {a(n) = my(A, k); if( n<-1, 0, k = (sqrtint(40*n + 48) + 7)\10; A = x * (sum(i=-k, k, (-1)^i * x^((5*i^2 + 3*i)/2), x^2 * O(x^n)) / sum(i=-k, k, (-1)^i * x^((5*i^2 + i)/2), x^2 * O(x^n)))^5; polcoeff( 1 / A - 11 - A, n))};

Crossrefs

Cf. A007252, A121591.

Cf. A045483. [R. J. Mathar, Dec 13 2008]

Cf. A058511, A078905, A145466, A229793.

Sequence in context: A000729 A280666 A282937 * A132725 A338596 A121899

Adjacent sequences: A106245 A106246 A106247 * A106249 A106250 A106251

Keyword

sign

Author

Michael Somos, Apr 26 2005

Status

approved