A242373 Sum_{k=0..n} C(n,k) * (2*k+1)^(2*n).

1, 10, 788, 166712, 68475920, 46294050592, 46645589472064, 65553860981315968, 122544885380995907840, 294065070661381857417728, 881074796163065604590326784, 3223847668121045228481269463040, 14146460882056535042193752974692352

Offset: 0

Author

Vaclav Kotesovec, May 12 2014

Keywords

• nonn
• easy

Crossrefs

Cf. A222525, A242449.

Programs

Mathematica

Table[Sum[Binomial[n,k]*(2*k+1)^(2*n),{k,0,n}],{n,0,20}]

Formula

a(n) ~ 2^(2*n) * n^(2*n) * r^(2*n+1) / (sqrt(2-r) * exp(2*n) * (1-r)^(n+1/2)), where r = 2/(2+LambertW(2*exp(-2))) = 0.901829091937052... . - Vaclav Kotesovec, May 14 2014