A352377 Expansion of e.g.f. exp(1 - cos(x) + sin(x)).

1, 1, 2, 3, 5, 2, -17, -105, -302, -323, 2735, 21318, 74513, 5345, -1876118, -13036317, -35542499, 183591298, 2771934527, 14515620855, -4104116566, -739297426531, -6244977674825, -14587702161978, 240078040966369, 3207383844181633, 14652985540658834, -87474514259307453, -2013684557381588299

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..594

Formula

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

Mathematica

With[{m=40}, CoefficientList[Series[Exp[Sin[x]-Cos[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-1)\2)*binomial(n-1, k-1)*a(n-k)));
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 40);
Coefficients(R!(Laplace( Exp(Sin(x) -Cos(x) +1) ))); // G. C. Greubel, Jan 06 2026
(SageMath)
@CachedFunction
def A352377(n):
    if n==0: return 1
    else: return sum((-1)^((n-k-1)//2)*binomial(n-1, k)*A352377(k) for k in range(n))
print([A352377(n) for n in range(41)]) # G. C. Greubel, Jan 06 2026

Crossrefs

Cf. A002017, A260884, A352145.

Sequence in context: A113195 A069110 A238684 * A202694 A123221 A197032

Adjacent sequences: A352374 A352375 A352376 * A352378 A352379 A352380

Keyword

sign

Author

Seiichi Manyama, Mar 14 2022

Status

approved