|
%I #20 Feb 04 2024 12:41:17
%S 1,48,1224,21952,309876,3657312,37468928,341773440,2826752418,
%T 21491641808,151810235136,1004753937600,6273891838360,37171410206112,
%U 209969121051648,1135389617917568,5897908848093087,29521227582821520,142760699405228800
%N Expansion of Product_{m>=1} 1/(1-x^m)^48.
%H Seiichi Manyama, <a href="/A082558/b082558.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Alois P. Heinz)
%H <a href="/index/Pro#1mxtok">Index entries for expansions of Product_{k >= 1} (1-x^k)^m</a>
%p a:= proc(n) option remember; `if`(n=0, 1, add(
%p numtheory[sigma](j)*a(n-j), j=1..n)*48/n)
%p end:
%p seq(a(n), n=0..25); # _Alois P. Heinz_, Mar 12 2015
%t CoefficientList[1/QPochhammer[x]^48 + O[x]^100, x] (* _Jean-François Alcover_, Feb 04 2024 *)
%o (PARI) Vec(1/eta(x)^48 + O(x^30)) \\ _Michel Marcus_, Sep 17 2018
%Y Cf. 48th column of A144064.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, May 04 2003
| 