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%I #21 Mar 28 2022 07:42:54
%S 1,1,2,4,8,3,-124,-1306,-10144,-67723,-363392,-831672,16709824,
%T 386800759,5631873664,66256305994,619010054144,3201069236265,
%U -40479063835648,-1775812586063860,-39853546353553408,-694055641682352469,-9591063643658387456,-84103588142498507346
%N Expansion of e.g.f. 1/(1 - (sin(x) + x*cos(x))/2 ).
%H Seiichi Manyama, <a href="/A349104/b349104.txt">Table of n, a(n) for n = 0..466</a>
%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * (k+1) * binomial(n,2*k+1) * a(n-2*k-1).
%t With[{m = 23}, Range[0, m]! * CoefficientList[Series[1/(1 - (Sin[x] + x*Cos[x])/2), {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *)
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1-(sin(x)+x*cos(x))/2)))
%o (PARI) a(n) = if(n==0, 1, sum(k=0, (n-1)\2, (-1)^k*(k+1)*binomial(n, 2*k+1)*a(n-2*k-1)));
%Y Cf. A349103, A349105, A352252.
%K sign
%O 0,3
%A _Seiichi Manyama_, Mar 26 2022
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