A082558 Expansion of Product_{m>=1} 1/(1-x^m)^48.

1, 48, 1224, 21952, 309876, 3657312, 37468928, 341773440, 2826752418, 21491641808, 151810235136, 1004753937600, 6273891838360, 37171410206112, 209969121051648, 1135389617917568, 5897908848093087, 29521227582821520, 142760699405228800

Offset: 0

Author

N. J. A. Sloane, May 04 2003

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Alois P. Heinz)
• Index entries for expansions of Product_{k >= 1} (1-x^k)^m

Crossrefs

Cf. 48th column of A144064.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      numtheory[sigma](j)*a(n-j), j=1..n)*48/n)
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Mar 12 2015

Mathematica

CoefficientList[1/QPochhammer[x]^48 + O[x]^100, x] (* Jean-François Alcover, Feb 04 2024 *)

PARI

Vec(1/eta(x)^48 + O(x^30)) \\ Michel Marcus, Sep 17 2018