A397715 Self-convolution of hyperfactorials (A002109).

1, 2, 9, 224, 55528, 172856160, 8062329832848, 6639540860396371968, 111392882523018179554811904, 43155882557276614860795848294400000, 431558824501993007074816469828058115276800000, 123128769173701666727732924444625440015971414494412800000

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Formula

a(n) = Sum_{k=0..n} A002109(k)*A002109(n-k).

a(n) ~ 2*A * n^(n*(n+1)/2 + 1/12) / exp(n^2/4), where A is the Glaisher-Kinkelin constant A074962.

Mathematica

Table[Sum[Hyperfactorial[k]*Hyperfactorial[n-k], {k, 0, n}], {n, 0, 12}]

Crossrefs

Cf. A002109, A396841, A397718, A074962.

Sequence in context: A112311 A067564 A267408 * A359608 A165797 A011823

Adjacent sequences: A397694 A397695 A397700 * A397716 A397717 A397718

Keyword

nonn,new

Author

Vaclav Kotesovec, Jul 06 2026

Status

approved