A082559 G.f.: Product_{m>=1} 1/(1-x^m)^64.

1, 64, 2144, 49920, 905840, 13627264, 176638592, 2025205248, 20930373880, 197788352320, 1728062919232, 14083242424576, 107837287452608, 780481475916160, 5366307146732800, 35202669371599360, 221142159585764508, 1334633003840266624, 7760187771579170400

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) = 16777216 * exp(-8*Pi/3) * Gamma(3/4)^64 / Pi^16 = A388467. - 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)*64/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}]*64/n]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jan 13 2025, after Alois P. Heinz *)

Crossrefs

Cf. 64th column of A144064.

Sequence in context: A017727 A089458 A283280 * A008790 A183432 A017211

Adjacent sequences: A082556 A082557 A082558 * A082560 A082561 A082562

Keyword

nonn

Author

N. J. A. Sloane, May 04 2003

Status

approved