A234357 Array T(n,k) by antidiagonals: T(n,k) = n^k * Fibonacci(k).

1, 2, 2, 3, 8, 3, 4, 18, 24, 5, 5, 32, 81, 80, 8, 6, 50, 192, 405, 256, 13, 7, 72, 375, 1280, 1944, 832, 21, 8, 98, 648, 3125, 8192, 9477, 2688, 34, 9, 128, 1029, 6480, 25000, 53248, 45927, 8704, 55, 10, 162, 1536, 12005, 62208, 203125, 344064, 223074, 28160, 89, 11, 200, 2187

Offset

0,2

Links

Table of n, a(n) for n=0..57.

Formula

G.f. of n-th row: 1/(1 - n*x - n^2*x^2).

Recurrence: T(n,k) = n*T(n,k-1) + n^2*T(n,k-2), starting n, 2*n^2.

Example

Array starts:
1,  2,   3,    5,     8,     13,    21,   34, 55, 89,...    (A000045)
2,  8,  24,   80,   256,    832,  2688, 8704,...   (A063727, A085449)
3, 18,  81,  405,  1944,   9477, 45927,...         (A122069, A099012)
4, 32, 192, 1280,  8192,  53248,...                         (A099133)
5, 50, 375, 3125, 25000, 203125,...
6, 72, 648, 6480, 62208, 606528,...
...
Columns: A000027, A001105, A117642.

Prog

(PARI) T(n, k)=n^k*fibonacci(k)
(PARI) T(n, k)=polcoeff(Ser(1/(1-n*x-n^2*x^2)), k)

Crossrefs

Sequence in context: A296804 A296952 A141611 * A145596 A186753 A135835

Adjacent sequences: A234354 A234355 A234356 * A234358 A234359 A234360

Keyword

nonn,tabl

Author

Ralf Stephan, Dec 24 2013

Status

approved