A331615 E.g.f.: exp(1 / (1 - arcsin(x)) - 1).

1, 1, 3, 14, 85, 640, 5703, 58760, 685353, 8925632, 128231627, 2014061568, 34312150525, 630043097216, 12400033125647, 260357810321664, 5807790344591953, 137144754146230272, 3417248676737769619, 89590823377278496768, 2465026658283881339301

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) * A189780(k) * a(n-k).

Mathematica

nmax = 20; CoefficientList[Series[Exp[1/(1 - ArcSin[x]) - 1], {x, 0, nmax}], x] Range[0, nmax]!
A189780[0] = 1; A189780[n_] := A189780[n] = Sum[Binomial[n, k] If[OddQ[k], ((k - 2)!!)^2, 0] A189780[n - k], {k, 1, n}]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] A189780[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

Prog

(PARI) seq(n)={Vec(serlaplace(exp(1/(1 - asin(x + O(x*x^n))) - 1)))} \\ Andrew Howroyd, Jan 22 2020

Crossrefs

Cf. A006228, A189780, A189815, A331607, A331608, A331616, A331617, A331618.

Sequence in context: A088716 A005189 A331608 * A317060 A308940 A276313

Adjacent sequences: A331612 A331613 A331614 * A331616 A331617 A331618

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 22 2020

Status

approved