A191364 E.g.f. (1+x)^((1-sqrt(1-4*x))/(2*x)).

1, 1, 2, 15, 152, 2190, 39894, 886074, 23187632, 699092136, 23860707480, 909507899520, 38295831424872, 1765316863497720, 88423030108046256, 4782130014839166360, 277730241327729713280, 17239188136821392859840

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: A396558 A325060 A002103 * A308379 A381784 A373357

Adjacent sequences: A191361 A191362 A191363 * A191365 A191366 A191367

Keyword

nonn

Author

Vladimir Kruchinin, May 31 2011

Status

approved