A354517 Expansion of e.g.f. cos(x)^exp(x).

1, 0, -1, -3, -5, 10, 134, 742, 2325, -2820, -118756, -1138368, -7132025, -20945990, 196411214, 4438271692, 50498101545, 400644382200, 1571151012344, -16415635331328, -500300343321365, -7486919544207050, -81415563206142166, -563533196469890228

Offset: 0

Author

Seiichi Manyama, Aug 16 2022

Keywords

• sign

Crossrefs

Cf. A000248, A009189, A215515, A354518, A354519.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(cos(x)^exp(x)))

PARI

a354519(n) = sum(k=1, n\2, ((-4)^k-(-16)^k)*bernfrac(2*k)/(2*k)*binomial(n, 2*k));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, a354519(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = -Sum_{k=1..n} A354519(k) * binomial(n-1,k-1) * a(n-k).