A082556 Expansion of g.f. Product_{m>=1} 1/(1-x^m)^30.

1, 30, 495, 5890, 56265, 456786, 3263990, 21017040, 124018290, 679118550, 3484681077, 16884109080, 77731521980, 341784289770, 1441489548195, 5852747363518, 22948550618400, 87131200662540, 321100847115950, 1150962640399770, 4020058004480100, 13704611801774340

Offset: 0

Author

N. J. A. Sloane, May 04 2003

Keywords

• nonn

Links

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

Crossrefs

Cf. 30th column of A144064.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      numtheory[sigma](j)*a(n-j), j=1..n)*30/n)
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Mar 12 2015

Mathematica

a[n_] := a[n] = If[n == 0, 1, Sum[DivisorSigma[1, j]*a[n-j], {j, 1, n}]*30/n];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jan 13 2025, after Alois P. Heinz *)