A351804 a(n) = [x^n] 1/Product_{j=1..n} (1 - j^n*x).

1, 1, 21, 28800, 6702928485, 485036145970949475, 17284020213927891173772415260, 439885788765576174397949231373608504971360, 10926401685584312222862714944076761452123218197332439365413, 346792877099311752547903589477147000220953930332269111366383185472249165168535

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..26

Formula

a(n) = Sum_{p in {1..n}^n : p_i <= p_{i+1}} Product_{j=1..n} p_j^n.

a(n) ~ c * n^(n^2), where c = 1/QPochhammer(exp(-1)) = 1.98244090741... - Vaclav Kotesovec, May 13 2025

Example

a(2) = (1*1)^2 + (1*2)^2 + (2*2)^2 = 1 + 4 + 16 = 21.

Maple

b:= proc(n, k, p) option remember; `if`(k=0, 1,
      add(b(j, k-1, p)*j^p, j=1..n))
    end:
a:= n-> b(n$3):
seq(a(n), n=0..9);

Mathematica

Table[SeriesCoefficient[Product[1/(1 - k^n*x), {k, 1, n}], {x, 0, n}], {n, 0, 10}] (* Vaclav Kotesovec, May 13 2025 *)

Crossrefs

Cf. A036740, A351800.

Sequence in context: A250066 A299035 A189648 * A283841 A100414 A396673

Adjacent sequences: A351801 A351802 A351803 * A351805 A351806 A351807

Keyword

nonn

Author

Alois P. Heinz, Feb 19 2022

Status

approved