A144657 - OEIS

%I #19 Mar 13 2024 16:46:27

%S 0,2,14,62,242,912,3418,12854,48602,184736,705410,2704132,10400574,

%T 40116572,155117490,601080358,2333606186,9075135264,35345263762,

%U 137846528780,538257874398,2104098963676,8233430727554,32247603683052,126410606437702,495918532948052,1946939425648058

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

%H Vincenzo Librandi, <a href="/A144657/b144657.txt">Table of n, a(n) for n = 0..200</a>

%F 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

%F a(n) ~ 4^(n+1)/sqrt(Pi*n). - _Vaclav Kotesovec_, Oct 20 2012

%F a(n) = 2*A048775(n) for n>0. - _Hugo Pfoertner_, Mar 13 2024

%t Table[Sum[Sum[(i+j)!/i!/j!,{i,1,n}],{j,1,n}],{n,0,20}] (* corrected by _Vaclav Kotesovec_, Oct 20 2012 *)

%Y Suggested by a formula in A048775.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jan 30 2009