A351745 Expansion of e.g.f. cos(x) * exp(exp(x) - 1).

1, 1, 1, 2, 4, 7, 7, -47, -549, -4284, -30756, -218315, -1571731, -11603343, -88284675, -693810426, -5636074516, -47324368509, -410556832893, -3677474325071, -33983530496537, -323712524813480, -3175734966375132, -32058728131612719, -332733970940411623, -3547642104951509087

Offset: 0

Author

Ilya Gutkovskiy, Apr 07 2022

Keywords

• sign

Crossrefs

Cf. A000110, A009113, A224271, A352905.

Programs

Mathematica

nmax = 25; CoefficientList[Series[Cos[x] Exp[Exp[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[(-1)^k Binomial[n, 2 k] BellB[n - 2 k], {k, 0, Floor[n/2]}], {n, 0, 25}]

PARI

my(x='x+O('x^30)); Vec(serlaplace(cos(x)*exp(exp(x) - 1))) \\ Michel Marcus, Apr 09 2022

Formula

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