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A191364 E.g.f. (1+x)^((1-sqrt(1-4*x))/(2*x)). 0
1, 1, 2, 15, 152, 2190, 39894, 886074, 23187632, 699092136, 23860707480, 909507899520, 38295831424872, 1765316863497720, 88423030108046256, 4782130014839166360, 277730241327729713280, 17239188136821392859840 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = n! * sum(k=1..n, k*sum(i=0..n-k, (C(2*(k+i)-k-1,k+i-1) *stirling1(n-i,k))/ ((k+i)*(n-i)!))), n>0, a(0)=1.

a(n) ~ 25*log(5/4)*2^(2*n-7/2)*n^(n-1)/exp(n). - Vaclav Kotesovec, Jun 27 2013

MATHEMATICA

CoefficientList[Series[(1+x)^((1-Sqrt[1-4*x])/(2*x)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)

PROG

(Maxima) a(n):=n!*sum(k*sum((binomial(2*(k+i)-k-1, k+i-1)*stirling1(n-i, k))/ ((k+i)*(n-i)!), i, 0, n-k), k, 1, n);

CROSSREFS

Sequence in context: A001854 A060226 A002103 * A233832 A185756 A239107

Adjacent sequences:  A191361 A191362 A191363 * A191365 A191366 A191367

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, May 31 2011

STATUS

approved

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Last modified February 24 04:33 EST 2018. Contains 299595 sequences. (Running on oeis4.)