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

0,3

Links

Table of n, a(n) for n=0..23.

Formula

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

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

Crossrefs

Cf. A083859, A083861, A083862.

Sequence in context: A008485 A213684 A373930 * A267241 A162271 A164593

Adjacent sequences: A082294 A082295 A082296 * A082298 A082299 A082300

Keyword

easy,nonn

Author

Paul Barry, May 06 2003

Status

approved