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
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Programs
-
Mathematica
nmax = 20; CoefficientList[Series[Product[(1 + x^k)^48, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)
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