%I #15 Aug 18 2022 10:19:33
%S 1,1,3,4,9,-24,-143,-902,-1631,5176,109841,664302,1479841,-16079764,
%T -240229975,-1395162974,126628545,101950486736,1118811398113,
%U 4468008939542,-46600859353919,-1019505781080044,-7952038289388071,10041106628453162
%N Expansion of e.g.f. exp(x)^( cos(x) + sin(x) ).
%F a(0) = 1; a(n) = Sum_{k=1..n} (-1)^floor((k-1)/2) * k * binomial(n-1,k-1) * a(n-k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)^(cos(x)+sin(x))))
%o (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;
%Y Cf. A000248, A009189, A009214, A354546.
%K sign
%O 0,3
%A _Seiichi Manyama_, Aug 18 2022