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

%I #17 Jul 10 2021 06:13:49

%S 1,2,9,78,1141,25442,804309,34227438,1886573641,130746521282,

%T 11127809595009,1141012634368398,138730500808639741,

%U 19735099323279743522,3247323803322747092109,611982206046097666022958

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

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

%F 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

%t 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 *)

%t 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 *)

%Y Cf. A103327, A002084, A000364.

%K easy,nonn

%O 0,2

%A _Philippe Deléham_, Oct 24 2005

%E More terms from _Robert G. Wilson v_, Oct 24 2005