A349104 Expansion of e.g.f. 1/(1 - (sin(x) + x*cos(x))/2 ).

1, 1, 2, 4, 8, 3, -124, -1306, -10144, -67723, -363392, -831672, 16709824, 386800759, 5631873664, 66256305994, 619010054144, 3201069236265, -40479063835648, -1775812586063860, -39853546353553408, -694055641682352469, -9591063643658387456, -84103588142498507346

Offset: 0

Author

Seiichi Manyama, Mar 26 2022

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..466

Crossrefs

Cf. A349103, A349105, A352252.

Programs

Mathematica

With[{m = 23}, Range[0, m]! * CoefficientList[Series[1/(1 - (Sin[x] + x*Cos[x])/2), {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1-(sin(x)+x*cos(x))/2)))

PARI

a(n) = if(n==0, 1, sum(k=0, (n-1)\2, (-1)^k*(k+1)*binomial(n, 2*k+1)*a(n-2*k-1)));

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * (k+1) * binomial(n,2*k+1) * a(n-2*k-1).