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
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..484
Programs
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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