A354545 Expansion of e.g.f. exp(x)^( cos(x) + sin(x) ).
1, 1, 3, 4, 9, -24, -143, -902, -1631, 5176, 109841, 664302, 1479841, -16079764, -240229975, -1395162974, 126628545, 101950486736, 1118811398113, 4468008939542, -46600859353919, -1019505781080044, -7952038289388071, 10041106628453162
Offset: 0
Keywords
Programs
-
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)^(cos(x)+sin(x)))) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (-1)^((j-1)\2)*j*binomial(i-1, j-1)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^floor((k-1)/2) * k * binomial(n-1,k-1) * a(n-k).