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
Keywords
Examples
a(2) = (1*1)^2 + (1*2)^2 + (2*2)^2 = 1 + 4 + 16 = 21.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..26
Programs
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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 *)
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