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A331618 E.g.f.: exp(1 / (1 - arctanh(x)) - 1). 3
1, 1, 3, 15, 97, 785, 7523, 83615, 1053281, 14838177, 230832867, 3929944623, 72633052545, 1447981700529, 30960823851267, 706676217730239, 17145815895371073, 440594781536265537, 11952178787661839427, 341291300477569866831, 10231558345117929439521 (list; graph; refs; listen; history; text; internal format)
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) * A296676(k) * a(n-k).

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

MATHEMATICA

nmax = 20; CoefficientList[Series[Exp[1/(1 - ArcTanh[x]) - 1], {x, 0, nmax}], x] Range[0, nmax]!

A296676[0] = 1; A296676[n_] := A296676[n] = Sum[Binomial[n, k] If[OddQ[k], (k - 1)!, 0] A296676[n - k], {k, 1, n}]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] A296676[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

PROG

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

CROSSREFS

Cf. A000246, A080833, A202139, A296676, A331610, A331615, A331616, A331617.

Sequence in context: A331325 A132437 A331610 * A128081 A186264 A140286

Adjacent sequences:  A331615 A331616 A331617 * A331619 A331620 A331621

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 22 2020

STATUS

approved

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Last modified September 28 08:33 EDT 2020. Contains 337394 sequences. (Running on oeis4.)