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A191365 E.g.f. (1/(1-x))^exp(x) 2
1, 1, 4, 18, 102, 695, 5485, 49077, 490308, 5404569, 65106103, 850535477, 11972432846, 180605413001, 2906109200293, 49678357272247, 898988188301320, 17167497793440977, 344991795682802331, 7277230501449340417, 160765066207998479698 (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=1..n, sum(i=0..n-k, binomial(n,i)*k^i*(-1)^(n-k-i)*stirling1(n-i,k))), n>0, a(0)=1.

a(n) ~ n! * n^(exp(1)-1)/Gamma(exp(1)) * (1-exp(1)*(exp(1)-1)*log(n)/n). - Vaclav Kotesovec, Jun 21 2013

MATHEMATICA

CoefficientList[Series[(1/(1-x))^Exp[x], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 21 2013 *)

PROG

(Maxima) a(n):=sum(sum(binomial(n, i)*k^i*(-1)^(n-k-i)*stirling1(n-i, k), i, 0, n-k), k, 1, n);

CROSSREFS

Sequence in context: A201826 A064852 A229286 * A159666 A316186 A231274

Adjacent sequences:  A191362 A191363 A191364 * A191366 A191367 A191368

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, May 31 2011

STATUS

approved

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Last modified October 14 07:19 EDT 2019. Contains 327995 sequences. (Running on oeis4.)