OFFSET
0,2
LINKS
Robert Israel, Table of n, a(n) for n = 0..531
FORMULA
Appears to satisfy recurrence
a(n+3) = (12 + 11 n + 2 n^2) a(n+2) + (5 n + 2 n^2) a(n+1) - a(n) + 8
corresponding to differential equation for g.f.
(5*t^2-2*t^3-3*t^4)*(d/dt)a(t)-2*t^3*(-1+t^2)*(d^2/dt^2)a(t)+(-1-t-t^2+2*t^3+t^4)*a(t)+1+3*t+3*t^2+t^3.
Apparently also a(n) + (-2*n^2+n+2)*a(n-1) + (2*n-3)*a(n-2) +(2*n^2-11*n+13)*a(n-3) - a(n-4) = 0. - R. J. Mathar, May 19 2014
a(n) ~ sqrt(Pi) * 2^(n+1) * n^(2*n + 1/2) / exp(2*n). - Vaclav Kotesovec, Dec 20 2017
EXAMPLE
a(2) = 4!/(4*0!) + 3!/(2*1!) + 2!/(1*2!) = 10.
MAPLE
A:= n -> add((2*n-k)!*2^(k-n)/k!, k=0..n)
MATHEMATICA
Table[Sum[(n+k)! / (2^k * (n-k)!), {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Dec 20 2017 *)
PROG
(PARI) a(n)=sum(k=0, n, (2*n-k)!<<(k-n)/k!) \\ Charles R Greathouse IV, Jan 03 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Israel, Dec 30 2011
STATUS
approved