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%I #27 Mar 16 2022 11:46:43
%S 1,1,0,-3,-5,12,71,7,-1028,-2573,14793,100188,-128831,-3445791,
%T -5741800,113954461,601512787,-3296210612,-41316895641,37322755431,
%U 2570678600548,6983413204755,-149303353515823,-1080122148248420,7405149869523649,119115584584019713
%N Expansion of e.g.f. exp(-1 + cos(x) + sin(x)).
%H Seiichi Manyama, <a href="/A352145/b352145.txt">Table of n, a(n) for n = 0..586</a>
%F a(0) = 1; a(n) = Sum_{k=1..n} (-1)^floor(k/2) * binomial(n-1,k-1) * a(n-k).
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(-1+cos(x)+sin(x))))
%o (PARI) a(n) = if(n==0, 1, sum(k=1, n, (-1)^(k\2)*binomial(n-1, k-1)*a(n-k)));
%Y Cf. A002017, A005046, A292935, A352377.
%K sign
%O 0,4
%A _Seiichi Manyama_, Mar 15 2022