A302557 -id:A302557 - cp's OEIS frontend

A305275 Coefficients in asymptotic expansion of sequence A302557.

1, 0, 2, 6, 35, 256, 2187, 21620, 243947, 3098528, 43799819, 682540780, 11630529643, 215190967544, 4296657514283, 92083313483300, 2108244638675035, 51350077108834832, 1325682930813985547, 36157047428501464220, 1038793351537388253211, 31354977545074731373512

Offset: 0

Vaclav Kotesovec, Aug 18 2018

nonn

			A302557(n) / (exp(-1) * n!) ~ 1 + 2/n^2 + 6/n^3 + 35/n^4 + 256/n^5 + 2187/n^6 + ...

Vaclav Kotesovec, Table of n, a(n) for n = 0..75

Cf. A256168, A260491, A260503, A260530, A260532, A260578, A260948, A260949, A260950, A302557.

a(k) ~ k! / (2 * exp(1) * (log(2))^(k+1)).

A328007 Expansion of e.g.f. 1 / (2 - exp(-x) / (1 - x)).

Original entry on oeis.org

1, 0, 1, 2, 15, 84, 705, 6222, 65779, 765608, 9999333, 143009250, 2235857943, 37833382716, 689729792713, 13469761663862, 280613761282875, 6211105772020560, 145566258957724845, 3601055676894146442, 93772841089130278495, 2563969299245947753700, 73443322391840827563921

Offset: 0

Ilya Gutkovskiy, Oct 01 2019

nonn

Cf. A000166, A002866, A302557, A321989, A328008.

nmax = 22; CoefficientList[Series[1/(2 - Exp[-x]/(1 - x)), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Subfactorial[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 22}]

my(x='x+O('x^25)); Vec(serlaplace(1 / (2 - exp(-x) / (1 - x)))) \\ Michel Marcus, Oct 02 2019

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A000166(k) * a(n-k).

a(n) ~ n! * (-LambertW(-exp(-1)/2) / (2*(1 + LambertW(-exp(-1)/2))^(n+2))). - Vaclav Kotesovec, Oct 02 2019

cp's OEIS Frontend

A305275 Coefficients in asymptotic expansion of sequence A302557.

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A328007 Expansion of e.g.f. 1 / (2 - exp(-x) / (1 - x)).

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