A352145 Expansion of e.g.f. exp(-1 + cos(x) + sin(x)).

1, 1, 0, -3, -5, 12, 71, 7, -1028, -2573, 14793, 100188, -128831, -3445791, -5741800, 113954461, 601512787, -3296210612, -41316895641, 37322755431, 2570678600548, 6983413204755, -149303353515823, -1080122148248420, 7405149869523649, 119115584584019713

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..586

Formula

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

Mathematica

With[{m=40}, CoefficientList[Series[Exp[Cos[x]+Sin[x]-1], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, Jan 06 2026 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(-1+cos(x)+sin(x))))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, (-1)^(k\2)*binomial(n-1, k-1)*a(n-k)));
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 40);
Coefficients(R!(Laplace( Exp(Cos(x) +Sin(x) -1) ))); // G. C. Greubel, Jan 06 2026
(SageMath)
@CachedFunction
def A352145(n):
    if n==0: return 1
    else: return sum((-1)^(k//2)*binomial(n-1, k-1)*A352145(n-k) for k in range(1, n+1))
print([A352145(n) for n in range(31)]) # G. C. Greubel, Jan 06 2026

Crossrefs

Cf. A002017, A005046, A292935, A352377.

Sequence in context: A307146 A293599 A156436 * A276735 A099791 A301901

Adjacent sequences: A352142 A352143 A352144 * A352146 A352147 A352148

Keyword

sign

Author

Seiichi Manyama, Mar 15 2022

Status

approved