A174826 Hankel transform of median Euler numbers A000657.

1, 3, 1260, 471517200, 550527639742080000, 5190428828598394601457507916800, 850896871373200757118814347241271815302935592960, 4613713947380451287616678748167888181805816329703795184496036199596032

Offset

0,2

Links

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

Formula

a(n)=Product{k=0..n, ((k+1)(4k+1)(4k+3)floor((2k+3)/2))^(n-k)}.

a(n) ~ sqrt(Gamma(1/4)) * 2^(2*n^2 + 7*n/2 + 9/8) * n^(n*(2*n+3) + 47/48) * Pi^(n + 3/4) / (A^(7/4) * exp(3*n*(n+1) - 7/48)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Feb 24 2019

Mathematica

Table[Product[((k+1)*(4*k+1)*(4*k+3)*Floor[(2*k+3)/2])^(n-k), {k, 0, n}], {n, 0, 10}] (* Vaclav Kotesovec, Feb 24 2019 *)

Crossrefs

Sequence in context: A034315 A172924 A129078 * A122389 A036066 A262516

Adjacent sequences: A174823 A174824 A174825 * A174827 A174828 A174829

Keyword

easy,nonn

Author

Paul Barry, Mar 30 2010

Status

approved