A217061 E.g.f. exp(A006351(x)).

1, 1, 3, 15, 109, 1053, 12767, 186763, 3204313, 63128665, 1404963387, 34867190823, 954800951749, 28600649870133, 930325531322519, 32658109219519843, 1230609634110271921, 49545182501048868145

Offset

0,3

Links

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

Formula

a(n) = sum(m=1..n, (sum(k=0..n-m, (n+k-1)!*sum(j=0..k, 1/(k-j)!*sum(l=0..j, (2^(j-l)*(-1)^(l+j)*stirling1(n-m-l+j,j-l))/(l!*(n-m-l+j)!)))))/(m-1)!), n>0, a(0)=1.

E.g.f.: 4*LambertW(-exp((x-1)/2)/2)^2 / exp(x). - Vaclav Kotesovec, Aug 04 2014

a(n) ~ sqrt(2) * n^(n-1) / (exp(n-1) * (2*log(2)-1)^(n-1/2)). - Vaclav Kotesovec, Aug 04 2014

Mathematica

CoefficientList[Series[4*ProductLog[-E^((x-1)/2)/2]^2/E^x, {x, 0, 15}], x]*Range[0, 15]! (* Vaclav Kotesovec, Aug 04 2014 *)

Prog

(Maxima)
a(n):=(sum((m*sum((n+k-1)!*sum(1/(k-j)!*sum((2^(j-l)*(-1)^(l+j)*stirling1(n-m-l+j, j-l))/(l!*(n-m-l+j)!), l, 0, j), j, 0, k), k, 0, n-m))/m!, m, 1, n));

Crossrefs

Sequence in context: A366180 A153305 A110328 * A054201 A090355 A083483

Adjacent sequences: A217058 A217059 A217060 * A217062 A217063 A217064

Keyword

nonn

Author

Vladimir Kruchinin, Sep 26 2012

Status

approved