A025233 - OEIS

%I #18 Feb 15 2018 08:12:57

%S 1,48,1176,19648,252204,2655456,23901760,189208704,1344644814,

%T 8713158928,52107076128,290374290624,1519725061816,7518508799904,

%U 35352238216704,158716136933504,683059486979301,2827559773199856

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

%H G. C. Greubel, <a href="/A025233/b025233.txt">Table of n, a(n) for n = 0..1000</a>

%F 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

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

%Y Cf. A022596, A022600.

%K nonn

%O 0,2

%A _N. J. A. Sloane_