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

Author

Seiichi Manyama, Mar 14 2022

Keywords

• sign

Links

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

Crossrefs

Cf. A002017, A260884.

Programs

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)));

Formula

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