A111196 a(n) = 2^(-n)*Sum_{k=0..n} binomial(2*n+1, 2*k+1)*A000364(n-k).

1, 2, 9, 78, 1141, 25442, 804309, 34227438, 1886573641, 130746521282, 11127809595009, 1141012634368398, 138730500808639741, 19735099323279743522, 3247323803322747092109, 611982206046097666022958

Offset: 0

Author

Philippe Deléham, Oct 24 2005

Keywords

• easy
• nonn

Crossrefs

Cf. A103327, A002084, A000364.

Programs

Mathematica

t = Range[0, 32]!CoefficientList[ Series[ Sec[x], {x, 0, 32}], x]; f[n_] := 2^(-n)*Sum [Binomial[2n + 1, 2k + 1]*t[[2n - 2k + 1]], {k, 0, n}]; Table[ f[n], {n, 0, 16}] (* Robert G. Wilson v, Oct 24 2005 *)
Table[Sum[Binomial[2*n + 1, 2*k + 1]*Abs[EulerE[2*(n-k)]], {k, 0, n}] / 2^n, {n, 0, 20}] (* Vaclav Kotesovec, Jul 10 2021 *)

Formula

a(n) = 2^(-n)*A002084(n).

a(n) ~ sinh(Pi/2) * 2^(3*n + 5) * n^(2*n + 3/2) / (Pi^(2*n + 3/2) * exp(2*n)). - Vaclav Kotesovec, Jul 10 2021

Extensions

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