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

Offset

0,2

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. [From Geoffrey Critzer, Apr 20 2009]

Links

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

Formula

a(n)=n!+(sum(m=0..n, sum(k=1..m, (binomial(k,m-k)*2^(k-m))/k!)))*n!. [From Vladimir Kruchinin, Jul 02 2011]

D-finite with recurrence a(n) = (n+1)*a(n-1) - (n-2)*(n-1)*a(n-3) . - Vaclav Kotesovec, Oct 20 2012

a(n) ~ n!*exp(3/2) . - Vaclav Kotesovec, Oct 20 2012

Mathematica

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

Prog

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

Crossrefs

Cf. A130905.

Sequence in context: A328500 A180389 A177389 * A054096 A006183 A189844

Adjacent sequences: A130904 A130905 A130906 * A130908 A130909 A130910

Keyword

nonn

Author

Karol A. Penson, Jun 08 2007

Extensions

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

Status

approved