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
KEYWORD
nonn
AUTHOR
Karol A. Penson, Jun 08 2007
EXTENSIONS
I deleted the initial 1. - Geoffrey Critzer, Apr 19 2009
STATUS
approved