A137704 - OEIS

A137704

Hankel transform of aerated factorial numbers.

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

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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