A025233 Expansion of Product_{m>=1} (1 + q^m)^48.

1, 48, 1176, 19648, 252204, 2655456, 23901760, 189208704, 1344644814, 8713158928, 52107076128, 290374290624, 1519725061816, 7518508799904, 35352238216704, 158716136933504, 683059486979301, 2827559773199856

Offset

0,2

Links

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

Formula

a(n) ~ exp(4*Pi*sqrt(n)) / (2^(49/2) * n^(3/4)) * (1 + (4*Pi - 3/(32*Pi))/sqrt(n)). - Vaclav Kotesovec, Nov 10 2017

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/64) * exp(2 * Pi) = A388371. - Simon Plouffe, Sep 15 2025

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 + x^k)^48, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)

Crossrefs

Cf. A022596, A022600.

Sequence in context: A344401 A369561 A011000 * A390442 A004425 A082558

Adjacent sequences: A025230 A025231 A025232 * A025234 A025235 A025236

Keyword

nonn

Author

N. J. A. Sloane

Status

approved