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Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(4*k+5) / (4*k+5)! ).
3

%I #17 Sep 23 2023 07:26:26

%S 1,0,0,0,0,1,0,0,0,1,252,0,0,1,4004,756756,0,1,65756,69837768,

%T 11732745024,1,1047508,5772957036,3957845988096,623360743125121,

%U 16781260,475191562560,1078063276530240,587517500395425601,88832646060056769732,38604505286340

%N Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(4*k+5) / (4*k+5)! ).

%F a(0) = 1; a(n) = Sum_{k=0..floor((n-5)/4)} binomial(n,4*k+5) * a(n-4*k-5).

%F E.g.f.: 1 / ( 1 + x - (sinh(x) + sin(x))/2 ).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1+x-(sinh(x)+sin(x))/2)))

%Y Cf. A245790, A365915, A365916.

%Y Cf. A352429, A365911.

%Y Cf. A365898.

%K nonn,easy

%O 0,11

%A _Seiichi Manyama_, Sep 23 2023