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A305981 Expansion of e.g.f. 1/(1 + LambertW(log(1 - x))). 1
1, 1, 5, 41, 468, 6854, 122582, 2589978, 63129392, 1743732192, 53827681152, 1836453542472, 68620052332752, 2786929842106344, 122241516227220504, 5758920745460806824, 290017142065771138560, 15547326972257789803200, 883974436758296523437760, 53131928820278417749940544, 3366145488853852112016117504 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) = Sum_{k=0..n} |Stirling1(n,k)|*k^k.

a(n) ~ n^n / ((exp(exp(-1)) - 1)^(n + 1/2) * exp(n*(1 - exp(-1)) + 1/2)). - Vaclav Kotesovec, Aug 18 2018

MAPLE

a:=series(1/(1+LambertW(log(1-x))), x=0, 21): seq(n!*coeff(a, x, n), n=0..20); # Paolo P. Lava, Mar 26 2019

MATHEMATICA

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

Join[{1}, Table[Sum[Abs[StirlingS1[n, k]] k^k, {k, n}], {n, 20}]]

CROSSREFS

Cf. A000312, A052807, A277489, A282190, A305819.

Sequence in context: A096364 A210661 A049119 * A032188 A240996 A143415

Adjacent sequences:  A305978 A305979 A305980 * A305982 A305983 A305984

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 18 2018

STATUS

approved

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Last modified November 12 09:01 EST 2019. Contains 329052 sequences. (Running on oeis4.)