A169976 Expansion of (psi(x)^24 + psi(-x)^24) / 2 in powers of x^2 where psi() is a Ramanujan theta function.

1, 276, 11178, 177400, 1612875, 10131156, 48897678, 193740408, 658523925, 1980143600, 5386270686, 13477895856, 31425764410, 68969957700, 143635113000, 285718115112, 545796171084, 1005775268868, 1794713445350, 3111031518000

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = (A013959(2*n + 3) - A000594(2*n + 3)) / 176896 = A014809(2*n).

Example

1 + 276*x + 11178*x^2 + 177400*x^3 + 1612875*x^4 + 10131156*x^5 + ...
q^3 + 276*q^5 + 11178*q^7 + 177400*q^9 + 1612875*q^11 + 10131156*q^13 + ...

Mathematica

QP:= Pochhammer; a[n_]:= SeriesCoefficient[(QP[q, q])^24*(QP[-q^(1/2), q^(1/2)]^24 + QP[q^(1/2), -q^(1/2)]^24)/2, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Apr 04 2018 *)

Prog

(PARI) {a(n) = local(A); if( n<0, 0, n *= 2; A = x * O(x^n); polcoeff( (eta(x^2 + A)^2 / eta(x + A))^24, n))}
(PARI) {a(n) = if( n<0, 0, n = 2*n + 3; (sigma(n, 11) - polcoeff( x * eta(x + x * O(x^n))^24, n)) / 176896 )}

Crossrefs

Sequence in context: A107080 A333049 A297525 * A297755 A166192 A186466

Adjacent sequences: A169973 A169974 A169975 * A169977 A169978 A169979

Keyword

nonn

Author

Michael Somos, Aug 15 2010

Status

approved