A082297 Main diagonal of array A083861.

0, 1, 5, 22, 105, 551, 3125, 18901, 120785, 809956, 5669525, 41253125, 310968905, 2421594449, 19434554165, 160416509794, 1359425390625, 11809173506531, 105013666399445, 954781355707373, 8865807366284825, 83996265859375000, 811222567266570805, 7980019803318567233

Offset: 0

Author

Paul Barry, May 06 2003

Keywords

• easy
• nonn

Crossrefs

Cf. A083859, A083861, A083862.

Programs

Maple

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;
seq(T(n, n), n = 0..40); # Petros Hadjicostas, Dec 25 2019

Formula

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