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

Author

Seiichi Manyama, Mar 15 2022

Keywords

• sign

Links

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

Crossrefs

Cf. A002017, A005046, A292935, A352377.

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\2)*binomial(n-1, k-1)*a(n-k)));

Formula

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