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

1, 2, 5, 15, 53, 217, 1015, 5355, 31513, 204857, 1458875, 11299695, 94600373, 851419597, 8198959735, 84124450035, 916270051633, 10559066809937, 128362804540595, 1641730799916375, 22037407161945293, 309782122281453877, 4551072446448773455, 69747642031977698715

Offset: 0

Author

Ilya Gutkovskiy, Oct 24 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..484

Crossrefs

Cf. A000111, A000667, A186364, A330046, A348587.

Programs

Maple

b:= proc(u, o) option remember; `if`(u+o=0, 1,
      add(b(o-1+j, u-j), j=1..u))
    end:
a:= n-> add(binomial(n, k)*b(k+1, 0), k=0..n):
seq(a(n), n=0..23);  # Alois P. Heinz, Oct 24 2021

Mathematica

nmax = 23; CoefficientList[Series[Exp[x]/(1 - Sin[x]), {x, 0, nmax}], x] Range[0, nmax]!

PARI

my(x='x+O('x^40)); Vec(serlaplace(exp(x)/(1-sin(x)))) \\ Michel Marcus, Oct 24 2021

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A000111(k+1).

a(n) ~ 2^(n + 7/2) * n^(n + 3/2) / (Pi^(n + 3/2) * exp(n - Pi/2)). - Vaclav Kotesovec, Oct 25 2021