A332255 E.g.f.: 1 / (2 - 1 / (2 + x - exp(x))).

1, 0, 1, 1, 13, 41, 461, 2745, 32397, 288937, 3794605, 44758649, 665371565, 9660560937, 162652002189, 2782536864697, 52737562595917, 1033546861769513, 21867683869860845, 481630083492884601, 11277805333488014445, 275314710164399079337, 7077059249870048306125

Offset

0,5

Links

Table of n, a(n) for n=0..22.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A032032(k) * a(n-k).

a(n) ~ n! * 2^(n-1) / ((c-1) * (2*c-3)^(n+1)), where c = -LambertW(-1, -exp(-3/2)) = 2.3576766739458990584... - Vaclav Kotesovec, Feb 08 2020

Mathematica

nmax = 22; CoefficientList[Series[1/(2 - 1/(2 + x - Exp[x])), {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) seq(n)={Vec(serlaplace(1/(2 - 1 / (2 + x - exp(x + O(x*x^n))))))} \\ Andrew Howroyd, Feb 08 2020

Crossrefs

Cf. A000670, A032032, A050351, A097236.

Sequence in context: A102130 A080186 A287307 * A201121 A116153 A116209

Adjacent sequences: A332252 A332253 A332254 * A332256 A332257 A332258

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 08 2020

Status

approved