A082297 - OEIS

%I #10 Dec 26 2019 04:46:34

%S 0,1,5,22,105,551,3125,18901,120785,809956,5669525,41253125,310968905,

%T 2421594449,19434554165,160416509794,1359425390625,11809173506531,

%U 105013666399445,954781355707373,8865807366284825,83996265859375000,811222567266570805,7980019803318567233

%N Main diagonal of array A083861.

%F a(n) = (((5 + sqrt(4*n + 1))/2)^n - ((5 - sqrt(4*n + 1))/2)^n)/sqrt(4*n + 1).

%p T := proc(n, k) local v; option remember; if 0 <= n and k = 0 then v := 0; end if; if 0 <= n and k = 1 then v := 1; end if; if 0 <= n and 2 <= k then v := 5*T(n, k - 1) + (n - 6)*T(n, k - 2); end if; v; end proc;

%p seq(T(n, n), n = 0..40); # _Petros Hadjicostas_, Dec 25 2019

%Y Cf. A083859, A083861, A083862.

%K easy,nonn

%O 0,3

%A _Paul Barry_, May 06 2003