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A256016 a(n) = n! * Sum_{k=1..n} k^n/k!. 4
1, 6, 57, 796, 15145, 374526, 11669665, 447595800, 20733553809, 1141067915290, 73552752257281, 5484203261135028, 467864288815609465, 45236104846954021014, 4915818294874879570305, 596044703812665607374256, 80118478395137652912476449, 11870487496575403846760198322 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..18.

FORMULA

a(n) ~ e*Bell(n)*n!, for the Bell numbers see A000110.

a(n) ~ sqrt(2*Pi) * n^(2*n+1/2) * exp(n/LambertW(n)-2*n) / (sqrt(1+LambertW(n)) * LambertW(n)^n).

MATHEMATICA

Table[n!*Sum[k^n/k!, {k, 1, n}], {n, 1, 20}]

CROSSREFS

Cf. A031971, A072034, A242446.

Sequence in context: A294511 A242817 A295238 * A145170 A180255 A034218

Adjacent sequences:  A256013 A256014 A256015 * A256017 A256018 A256019

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jun 01 2015

STATUS

approved

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Last modified June 6 03:03 EDT 2020. Contains 334858 sequences. (Running on oeis4.)