%I #2 Mar 30 2012 17:34:28
%S 2,3,3,2,14,2,2,25,25,2,2,49,60,49,2,2,115,126,126,115,2,2,217,253,
%T 514,253,217,2,2,415,506,1264,1264,506,415,2,2,810,517,3538,3388,3538,
%U 517,810,2,2,1602,561,8663,15416,15416,8663,561,1602,2
%N Triangular recursive sequence: a(n,k)=(n - k + 1)A(n - 1, k - 1) + (k)* A(n - 1, k) - 18*A(n - 2, k - 1).
%C Row sums are:
%C {2, 6, 18, 54, 162, 486, 1458, 4374, 13122, 52488,...}.
%F a(n,k)=(n - k + 1)A(n - 1, k - 1) + (k)* A(n - 1, k) - 18*A(n - 2, k - 1).
%e {2},
%e {3, 3},
%e {2, 14, 2},
%e {2, 25, 25, 2},
%e {2, 49, 60, 49, 2},
%e {2, 115, 126, 126, 115, 2},
%e {2, 217, 253, 514, 253, 217, 2},
%e {2, 415, 506, 1264, 1264, 506, 415, 2},
%e {2, 810, 517, 3538, 3388, 3538, 517, 810, 2},
%e {2, 1602, 561, 8663, 15416, 15416, 8663, 561, 1602, 2}
%t Clear[t, n, m, A];
%t A[2, 1] := A[2, 2] = 3;
%t A[3, 2] = 14;
%t A[4, 2] = 25; A[4, 3] = 25;
%t A[5, 2] = 49; A[5, 3] = 60; A[5, 4] = 49;
%t A[6, 2] = 115; A[6, 3] = 126; A[6, 4] = 126; A[6, 5] = 115;
%t A[7, 2] = 217; A[7, 3] = 253; A[7, 4] = 514; A[7, 5] = 253; A[7, 6] = 217;
%t A[8, 2] = 415; A[8, 3] = 506; A[8, 4] = 1264; A[8, 5] = 1264; A[8, 6] = 506; A[8, 7] = 415;
%t A[n_, 1] := 2; A[n_, n_] := 2;
%t A[n_, k_] := (n - k + 1)A[n - 1, k - 1] + (k)* A[n - 1, k] - 18*A[ n - 2, k - 1];
%t Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}]
%t Flatten[%] Table[Sum[A[n, m], {m, 1, n}], {n, 1, 10}];
%t Table[Sum[A[n, m], {m, 1, n}]/(2*3^(n - 1)), {n, 1, 10}]:
%K nonn,uned,tabl
%O 1,1
%A _Roger L. Bagula_, Dec 27 2008
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