A111195 a(n) = 2^(-n) * Sum_{k=0..n} binomial(2*n+1, 2*k+1) * A000364(k).

1, 2, 5, 26, 269, 4666, 121017, 4370722, 209364537, 12833657010, 979336390669, 91018760056938, 10120101446389765, 1326280083965014634, 202311875122389093761, 35535622109342844729074

Offset: 0

Author

Philippe Deléham, Oct 24 2005

Keywords

• easy
• nonn

Crossrefs

Cf. A000364, A103327, A308715.

Programs

Mathematica

t = Range[0, 34]!CoefficientList[ Series[ Sec[x], {x, 0, 34}], x]; f[n_] := 2^(-n)*Sum [Binomial[2n + 1, 2k + 1]*t[[2k + 1]], {k, 0, n}]; Table[ f[n], {n, 0, 17}] (* Robert G. Wilson v, Oct 24 2005 *)
Table[Sum[Binomial[2*n + 1, 2*k + 1]*Abs[EulerE[2*k]], {k, 0, n}] / 2^n, {n, 0, 20}] (* Vaclav Kotesovec, Jul 10 2021 *)

Formula

a(n) ~ cosh(Pi/2) * 2^(3*n + 3) * n^(2*n + 1/2) / (Pi^(2*n + 1/2) * exp(2*n)). - Vaclav Kotesovec, Jul 10 2021

Extensions

More terms from Robert G. Wilson v, Oct 24 2005