A144657 a(n) = Sum_{j = 1..n} Sum_{i = 1..n} (i + j)! / (i! * j!).

0, 2, 14, 62, 242, 912, 3418, 12854, 48602, 184736, 705410, 2704132, 10400574, 40116572, 155117490, 601080358, 2333606186, 9075135264, 35345263762, 137846528780, 538257874398, 2104098963676, 8233430727554, 32247603683052, 126410606437702, 495918532948052, 1946939425648058

Offset: 0

Author

N. J. A. Sloane, Jan 30 2009

Keywords

• nonn

Links

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

Crossrefs

Suggested by a formula in A048775.

Programs

Mathematica

Table[Sum[Sum[(i+j)!/i!/j!,{i,1,n}],{j,1,n}],{n,0,20}] (* corrected by Vaclav Kotesovec, Oct 20 2012 *)

Formula

Recurrence: (n+1)*(12*n-19)*a(n) = 2*(30*n^2 - 24*n - 19)*a(n-1) - (48*n^2 - 9*n - 7)*a(n-2) - 2*(2*n-3)*a(n-3). - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 4^(n+1)/sqrt(Pi*n). - Vaclav Kotesovec, Oct 20 2012

a(n) = 2*A048775(n) for n>0. - Hugo Pfoertner, Mar 13 2024