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A348580 Expansion of e.g.f. exp(x) / (1 - sin(x)).

%I A348580 #34 Nov 04 2021 18:29:45
%S A348580 1,2,5,15,53,217,1015,5355,31513,204857,1458875,11299695,94600373,
%T A348580 851419597,8198959735,84124450035,916270051633,10559066809937,
%U A348580 128362804540595,1641730799916375,22037407161945293,309782122281453877,4551072446448773455,69747642031977698715
%N A348580 Expansion of e.g.f. exp(x) / (1 - sin(x)).
%H A348580 Alois P. Heinz, <a href="/A348580/b348580.txt">Table of n, a(n) for n = 0..484</a>
%F A348580 a(n) = Sum_{k=0..n} binomial(n,k) * A000111(k+1).
%F A348580 a(n) ~ 2^(n + 7/2) * n^(n + 3/2) / (Pi^(n + 3/2) * exp(n - Pi/2)). - _Vaclav Kotesovec_, Oct 25 2021
%p A348580 b:= proc(u, o) option remember; `if`(u+o=0, 1,
%p A348580       add(b(o-1+j, u-j), j=1..u))
%p A348580     end:
%p A348580 a:= n-> add(binomial(n, k)*b(k+1, 0), k=0..n):
%p A348580 seq(a(n), n=0..23);  # _Alois P. Heinz_, Oct 24 2021
%t A348580 nmax = 23; CoefficientList[Series[Exp[x]/(1 - Sin[x]), {x, 0, nmax}], x] Range[0, nmax]!
%o A348580 (PARI) my(x='x+O('x^40)); Vec(serlaplace(exp(x)/(1-sin(x)))) \\ _Michel Marcus_, Oct 24 2021
%Y A348580 Cf. A000111, A000667, A186364, A330046, A348587.
%K A348580 nonn
%O A348580 0,2
%A A348580 _Ilya Gutkovskiy_, Oct 24 2021