A331607 E.g.f.: exp(1 / (1 - sin(x)) - 1).

1, 1, 3, 12, 61, 372, 2639, 21280, 191833, 1908688, 20750331, 244478784, 3100597333, 42088689216, 608543191559, 9332562964480, 151252803045937, 2582250195499264, 46306562212010355, 870011934425816064, 17086276243125287917

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

a(n) ~ 2^(n + 2/3) * exp(8/(3*Pi^2) - 5/6 + 2^(5/3) * n^(1/3) / Pi^(4/3) + 3 * 2^(1/3) * n^(2/3) / Pi^(2/3) - n) * n^(n - 1/6) / (sqrt(3) * Pi^(n + 1/3)). - Vaclav Kotesovec, Jan 26 2020

Mathematica

nmax = 20; CoefficientList[Series[Exp[1/(1 - Sin[x]) - 1], {x, 0, nmax}], x] Range[0, nmax]!
A000111[n_] := If[EvenQ[n], Abs[EulerE[n]], Abs[(2^(n + 1) (2^(n + 1) - 1) BernoulliB[n + 1])/(n + 1)]]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] A000111[k + 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

Crossrefs

Cf. A000111, A000772, A002017, A331608, A331610, A331611.

Sequence in context: A161799 A182970 A159925 * A235802 A317169 A121694

Adjacent sequences: A331604 A331605 A331606 * A331608 A331609 A331610

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 22 2020

Status

approved