%I #12 Dec 24 2013 09:35:42
%S 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,
%T 1944,832,21,8,98,648,3125,8192,9477,2688,34,9,128,1029,6480,25000,
%U 53248,45927,8704,55,10,162,1536,12005,62208,203125,344064,223074,28160,89,11,200,2187
%N Array T(n,k) by antidiagonals: T(n,k) = n^k * Fibonacci(k).
%F G.f. of n-th row: 1/(1 - n*x - n^2*x^2).
%F Recurrence: T(n,k) = n*T(n,k-1) + n^2*T(n,k-2), starting n, 2*n^2.
%e Array starts:
%e 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,... (A000045)
%e 2, 8, 24, 80, 256, 832, 2688, 8704,... (A063727, A085449)
%e 3, 18, 81, 405, 1944, 9477, 45927,... (A122069, A099012)
%e 4, 32, 192, 1280, 8192, 53248,... (A099133)
%e 5, 50, 375, 3125, 25000, 203125,...
%e 6, 72, 648, 6480, 62208, 606528,...
%e ...
%e Columns: A000027, A001105, A117642.
%o (PARI) T(n,k)=n^k*fibonacci(k)
%o (PARI) T(n,k)=polcoeff(Ser(1/(1-n*x-n^2*x^2)),k)
%K nonn,tabl
%O 0,2
%A _Ralf Stephan_, Dec 24 2013