A130907 E.g.f.: exp(x+x^2/2)/(1-x).

1, 2, 6, 22, 98, 516, 3172, 22436, 180252, 1624888, 16258376, 178877832, 2146674136, 27907332272, 390705042288, 5860585983856, 93769421948432, 1594080384922656, 28693447925921632, 545175515402212448, 10903510331802913056, 228973717087813867072

Offset: 0

Author

Karol A. Penson, Jun 08 2007

Keywords

• nonn

Comments

A jeweler creates collections of necklaces using exactly n different colored beads (to make the entire collection) then chooses some (or none or all) of the necklaces to sell. - Geoffrey Critzer, Apr 20 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A130905.

Programs

Mathematica

CoefficientList[Series[Exp[x + x^2/2 - Log[1 - x]], {x, 0, 21}], x]* Table[n!, {n, 0, 21}] (* Geoffrey Critzer, Apr 20 2009 *)

PARI

x='x+O('x^66);
egf=exp(x+x^2/2)/(1-x);
Vec(serlaplace(egf)) /* Joerg Arndt, Jul 11 2011 */

Formula

a(n) = n! + n!*Sum_{m=0..n} Sum_{k=1..m} binomial(k,m-k)*2^(k-m)/k!. - Vladimir Kruchinin, Jul 02 2011

From Vaclav Kotesovec, Oct 20 2012: (Start)

D-finite with recurrence a(n) = (n+1)*a(n-1) - (n-2)*(n-1)*a(n-3).

a(n) ~ n!*exp(3/2). (End)

Extensions

I deleted the initial 1. - Geoffrey Critzer, Apr 19 2009