A351804 - OEIS

%I #15 Feb 19 2022 12:21:37

%S 1,1,21,28800,6702928485,485036145970949475,

%T 17284020213927891173772415260,

%U 439885788765576174397949231373608504971360,10926401685584312222862714944076761452123218197332439365413,346792877099311752547903589477147000220953930332269111366383185472249165168535

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

%H Alois P. Heinz, <a href="/A351804/b351804.txt">Table of n, a(n) for n = 0..26</a>

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

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

%p b:= proc(n, k, p) option remember; `if`(k=0, 1,

%p       add(b(j, k-1, p)*j^p, j=1..n))

%p     end:

%p a:= n-> b(n$3):

%p seq(a(n), n=0..9);

%Y Cf. A036740, A351800.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Feb 19 2022