A366355 a(n) = (-1)^n * QPochhammer(n, n, n).

1, 0, 3, 416, 722925, 23205371904, 17674407688984375, 384914699001548351078400, 278893192683059452825059069034425, 7650586837724400321220283274999910891520000, 8900101000088880011112998877890031110997889100010099891

Offset

0,3

Links

Table of n, a(n) for n=0..10.

Eric Weisstein's World of Mathematics, q-Pochhammer Symbol.

Formula

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

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

Mathematica

Table[(-1)^n * QPochhammer[n, n, n], {n, 0, 12}]
Join[{1}, Table[Product[Sum[n^j, {j, 1, k}], {k, 1, n}] * (1 - 1/n)^n, {n, 1, 12}]]

Crossrefs

Cf. A023813.

Sequence in context: A305664 A152517 A333134 * A213001 A229751 A172859

Adjacent sequences: A366352 A366353 A366354 * A366356 A366357 A366358

Keyword

nonn

Author

Vaclav Kotesovec, Oct 08 2023

Status

approved