A082557 G.f.: Product_{m>=1} 1/(1-x^m)^32.

1, 32, 560, 7040, 70840, 604352, 4528832, 30529280, 188313180, 1076484640, 5759310304, 29064224896, 139226153920, 636391492800, 2787844780160, 11748015743232, 47774241056710, 187997792512640, 717605948122000, 2662641484567680, 9621587501598688, 33916687860860288

Offset

0,2

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

Formula

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = 4096 * exp(-4*Pi/3) * Gamma(3/4)^32 / Pi^8 = A388465. - Simon Plouffe, Sep 17 2025

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      numtheory[sigma](j)*a(n-j), j=1..n)*32/n)
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Mar 12 2015

Mathematica

With[{nn=30}, CoefficientList[Series[Product[1/(1-x^m)^32, {m, nn}], {x, 0, nn}], x]] (* Harvey P. Dale, Sep 04 2020 *)

Crossrefs

Cf. 32nd column of A144064.

Sequence in context: A233683 A093751 A178372 * A022660 A220631 A304308

Adjacent sequences: A082554 A082555 A082556 * A082558 A082559 A082560

Keyword

nonn

Author

N. J. A. Sloane, May 04 2003

Status

approved