OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..880
Adam M. Goyt and Lara K. Pudwell, Avoiding colored partitions of two elements in the pattern sense, arXiv:1203.3786 [math.CO], 2012. - From N. J. A. Sloane, Sep 17 2012
FORMULA
a(n) = Sum_{k=0..n} C(n, k)*floor(k/2)!.
E.g.f.: exp(x)*(1+sqrt(Pi)/2*(x+2)*exp(x^2/4)*erf(x/2)). - Vladeta Jovovic, Sep 25 2003
Conjecture: 2*a(n) -4*a(n-1) +(-n+2)*a(n-2) +(n-1)*a(n-3)=0. - R. J. Mathar, Nov 24 2012
a(n) ~ sqrt(Pi*n)/2 * exp(sqrt(2*n)-n/2-1/2)*(n/2)^(n/2) * (1+5/(3*sqrt(2*n))). - Vaclav Kotesovec, Aug 15 2013
MATHEMATICA
Table[Sum[Binomial[n, k]*Floor[k/2]!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 15 2013 *)
PROG
(PARI) for(n=0, 50, print1(sum(k=0, n, binomial(n, k)*(floor(k/2))!), ", ")) \\ G. C. Greubel, Feb 02 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 07 2003
STATUS
approved