A366355 - OEIS

%I #6 Feb 16 2025 08:34:06

%S 1,0,3,416,722925,23205371904,17674407688984375,

%T 384914699001548351078400,278893192683059452825059069034425,

%U 7650586837724400321220283274999910891520000,8900101000088880011112998877890031110997889100010099891

%N a(n) = (-1)^n * QPochhammer(n, n, n).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>.

%F For n>0, a(n) = (1 - 1/n)^n * Product_{k=1..n} Sum_{j=1..k} n^j.

%F a(n) ~ n^(n*(n+1)/2).

%t Table[(-1)^n * QPochhammer[n, n, n], {n, 0, 12}]

%t Join[{1}, Table[Product[Sum[n^j, {j, 1, k}], {k, 1, n}] * (1 - 1/n)^n, {n, 1, 12}]]

%Y Cf. A023813.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Oct 08 2023