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%I #10 Mar 23 2022 09:51:13
%S 1,1,2,6,24,121,732,5166,41664,378001,3810512,42253926,511139904,
%T 6698457481,94535404992,1429477706286,23056267551744,395120495014561,
%U 7169579673404672,137321623511274246,2768602189953629184,58609968225266985241,1299827736206335767552,30137364376923272989806
%N a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n,4*k+1) * a(n-4*k-1).
%H Seiichi Manyama, <a href="/A352429/b352429.txt">Table of n, a(n) for n = 0..449</a>
%F E.g.f.: 1 / (1 - Sum_{k>=0} x^(4*k+1) / (4*k+1)!).
%F E.g.f.: 1 / (1 - (sin(x) + sinh(x)) / 2).
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 4 k + 1] a[n - 4 k - 1], {k, 0, Floor[(n - 1)/4]}]; Table[a[n], {n, 0, 23}]
%t nmax = 23; CoefficientList[Series[1/(1 - Sum[x^(4 k + 1)/(4 k + 1)!, {k, 0, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\4, x^(4*k+1)/(4*k+1)!)))) \\ _Seiichi Manyama_, Mar 23 2022
%Y Cf. A000670, A006154, A243665, A291975, A306347, A352428, A352430.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Mar 16 2022
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