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A323630 Expansion of e.g.f. exp(log(1 - x)^2/2)/(1 - x). 0
1, 1, 3, 12, 62, 390, 2884, 24472, 234086, 2490030, 29139306, 371878056, 5138306700, 76398336924, 1215973642584, 20624305367520, 371309259462972, 7071037633297116, 141997246553420052, 2998654325698019280, 66426777891686458728, 1540117294435707244488, 37296711627004301923056 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) = Sum_{k=0..n} |Stirling1(n,k)|*A000085(k).

MAPLE

seq(n!*coeff(series(exp(log(1-x)^2/2)/(1-x), x=0, 23), x, n), n=0..22); # Paolo P. Lava, Jan 28 2019

MATHEMATICA

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

Table[Sum[Abs[StirlingS1[n, k]] HypergeometricU[-k/2, 1/2, -1/2]/(-1/2)^(k/2), {k, 0, n}], {n, 0, 22}]

PROG

(PARI) my(x='x + O('x^25)); Vec(serlaplace(exp(log(1 - x)^2/2)/(1 - x))) \\ Michel Marcus, Jan 24 2019

CROSSREFS

Cf. A000085, A004211, A008275, A130534, A319360.

Sequence in context: A187820 A074529 A143916 * A020033 A266329 A208734

Adjacent sequences:  A323626 A323627 A323629 * A323631 A323632 A323633

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 21 2019

STATUS

approved

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Last modified July 21 06:55 EDT 2019. Contains 325192 sequences. (Running on oeis4.)