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

Author

Michael Somos, Aug 15 2010

Keywords

• nonn

Examples

			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 + ...
		

Links

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

Crossrefs

Cf. A000594, A013959, A014809.

Programs

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 *)
a[n_] := (DivisorSigma[11, 2*n+3] - RamanujanTau[2*n+3]) / 176896; Array[a, 20, 0] (* Amiram Eldar, Jan 11 2025 *)

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 )}

Formula

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