A292190 Sum of n-th powers of products of terms in all partitions of n into distinct parts.

1, 1, 4, 35, 337, 11925, 371081, 49032439, 3545396034, 3416952655320, 749189363202730, 598250899004413536, 2383502427069445040595, 1729793152213690218766715, 131751643363739706679145099315, 271212858254426215135033141804302

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..98

Formula

a(n) = [x^n] Product_{k=1..n} (1 + k^n*x^k).

Example

5 = 4 + 1 = 3 + 2. So a(5) = 5^5 + (4*1)^5 + (3*2)^5 = 11925.

Maple

b:= proc(n, i, k) option remember; (m->
      `if`(m<n, 0, `if`(n=m, i!^k, b(n, i-1, k)+
      `if`(i>n, 0, i^k*b(n-i, i-1, k)))))(i*(i+1)/2)
    end:
a:= n-> b(n$3):
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 11 2017

Mathematica

nmax = 15; Table[SeriesCoefficient[Product[(1 + k^n*x^k), {k, 1, nmax}], {x, 0, n}], {n, 0, nmax}] (* Vaclav Kotesovec, Sep 12 2017 *)

Prog

(PARI) {a(n) = polcoeff(prod(k=1, n, 1+k^n*x^k+x*O(x^n)), n)}

Crossrefs

Main diagonal of A292189.

Cf. A265949, A292167, A292194, A292305, A292306.

Sequence in context: A174436 A145607 A188527 * A026304 A215541 A104456

Adjacent sequences: A292187 A292188 A292189 * A292191 A292192 A292193

Keyword

nonn

Author

Seiichi Manyama, Sep 11 2017

Status

approved