A137704 Hankel transform of aerated factorial numbers.

1, 1, 1, 2, 8, 96, 3456, 497664, 286654464, 825564856320, 11888133931008000, 1027134771639091200000, 532466665617704878080000000, 1932215036193527461576704000000000

Offset

0,4

Comments

Hankel transform of A084261. Hankel transform of A000142 (n!) with interpolated zeros.

a(n+1) is the Hankel transform of A003319 aerated. [From Paul Barry, Oct 07 2008]

Links

Table of n, a(n) for n=0..13.

Formula

a(n):=Product{k=0..n, floor((k+2)/2)^(n-k)};

a(n) ~ n^(n^2/2 + 3*n/2 + 7/6) * Pi^(n + 3/2) / (A^4 * 2^(n^2/2 + n/2 - 1/3) * exp(3*n^2/4 + 3*n/2 - 1/3)), where A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Jan 20 2024

Crossrefs

Sequence in context: A297332 A009752 A322736 * A001417 A156926 A361388

Adjacent sequences: A137701 A137702 A137703 * A137705 A137706 A137707

Keyword

easy,nonn

Author

Paul Barry, Feb 07 2008

Status

approved