A343845 a(n) = Sum_{k=0..floor(n/2)} A109449(n-k, k).

1, 1, 2, 4, 9, 27, 93, 392, 1898, 10493, 64885, 443916, 3326317, 27085015, 238073306, 2246348560, 22643042325, 242808804441, 2759740869777, 33138397797908, 419171443909394, 5570771017483187, 77603014042711369, 1130712331125929112, 17198408830271090233

Offset: 0

Author

Peter Luschny, May 06 2021

Keywords

• nonn

Crossrefs

Cf. A109449.

Programs

Maple

seq(add(A109449(n-k, k), k = 0..n/2), n = 0..25);

Mathematica

Table[Sum[Binomial[n-k,k] * 2^(n-2*k) * Abs[EulerE[n-2*k,1/2] + EulerE[n-2*k,1]], {k,0,Floor[n/2]}] - (1 + (-1)^n)/2, {n,0,25}] (* Vaclav Kotesovec, May 06 2021 *)

Formula

a(n) ~ 2^(n+2) * n! / Pi^(n+1). - Vaclav Kotesovec, May 06 2021