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A292190 Sum of n-th powers of products of terms in all partitions of n into distinct parts. 8
1, 1, 4, 35, 337, 11925, 371081, 49032439, 3545396034, 3416952655320, 749189363202730, 598250899004413536, 2383502427069445040595, 1729793152213690218766715, 131751643363739706679145099315, 271212858254426215135033141804302 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 20 18:08 EDT 2021. Contains 343135 sequences. (Running on oeis4.)