A169621 Hankel transform of quintuple factorial numbers A047055.

1, 10, 7000, 882000000, 37784880000000000, 890287342560000000000000000, 16991329795972963200000000000000000000000, 363197259318543010730772480000000000000000000000000000000

Offset

0,2

Links

Table of n, a(n) for n=0..7.

Formula

a(n)=Product{k=0..n, (floor(5(2k+1)/2)*floor(5(2k+2)/2))^(n-k)}=Product{k=0..n, (floor(5(2k+1)/2)*5(k+1))^(n-k)}.

a(n) ~ (2*Pi)^(n + 7/10) * 5^(n*(n+1)) * n^(n^2 + 7*n/5 + 31/75) / (A * Gamma(2/5)^(n + 2/5) * exp(3*n^2/2 + 7*n/5 - 1/12 - c)), where A is the Glaisher-Kinkelin constant A074962 and c = zeta'(-1, 2/5) = 0.0827672925828924139907562934385991589097620172389278574723... - Vaclav Kotesovec, Jan 23 2024

Mathematica

Table[Product[(Floor[5*(2*k+1)/2]*5*(k+1))^(n-k), {k, 0, n}], {n, 0, 10}] (* Vaclav Kotesovec, Jan 23 2024 *)

Crossrefs

Cf. A047055.

Sequence in context: A117803 A356041 A199520 * A121787 A304437 A358920

Adjacent sequences: A169618 A169619 A169620 * A169622 A169623 A169624

Keyword

easy,nonn

Author

Paul Barry, Dec 03 2009

Status

approved