login
Hankel transform of aerated factorial numbers.
3

%I #6 Jan 20 2024 12:18:13

%S 1,1,1,2,8,96,3456,497664,286654464,825564856320,11888133931008000,

%T 1027134771639091200000,532466665617704878080000000,

%U 1932215036193527461576704000000000

%N Hankel transform of aerated factorial numbers.

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

%C a(n+1) is the Hankel transform of A003319 aerated. [From _Paul Barry_, Oct 07 2008]

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

%F 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

%K easy,nonn

%O 0,4

%A _Paul Barry_, Feb 07 2008