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Expansion of e.g.f. exp(1 - cos(x) + sin(x)).
2

%I #14 Mar 15 2022 12:29:45

%S 1,1,2,3,5,2,-17,-105,-302,-323,2735,21318,74513,5345,-1876118,

%T -13036317,-35542499,183591298,2771934527,14515620855,-4104116566,

%U -739297426531,-6244977674825,-14587702161978,240078040966369,3207383844181633,14652985540658834,-87474514259307453,-2013684557381588299

%N Expansion of e.g.f. exp(1 - cos(x) + sin(x)).

%H Seiichi Manyama, <a href="/A352377/b352377.txt">Table of n, a(n) for n = 0..594</a>

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

%Y Cf. A002017, A260884.

%K sign

%O 0,3

%A _Seiichi Manyama_, Mar 14 2022