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%I #2 Mar 30 2012 17:34:29
%S 2,5,5,1,58,1,1,209,209,1,1,252,2854,252,1,1,309,14810,14810,309,1,1,
%T 382,33263,235108,33263,382,1,1,473,61455,1601271,1601271,61455,473,1,
%U 1,584,103948,5321656,29064422,5321656,103948,584,1,1,717,166968,13537664
%N A row sum triangular sequence: A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (n + 1)*(n + 2)*A(n - 2, k - 1).
%C Row sums are:(2*(n + 3)!)/4!:
%C {2, 10, 60, 420, 3360, 30240, 302400, 3326400, 39916800, 518918400,...}
%F A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (n + 1)*(n + 2)*A(n - 2, k - 1).
%e {2},
%e {5, 5},
%e {1, 58, 1},
%e {1, 209, 209, 1},
%e {1, 252, 2854, 252, 1},
%e {1, 309, 14810, 14810, 309, 1},
%e {1, 382, 33263, 235108, 33263, 382, 1},
%e {1, 473, 61455, 1601271, 1601271, 61455, 473, 1},
%e {1, 584, 103948, 5321656, 29064422, 5321656, 103948, 584, 1},
%e {1, 717, 166968, 13537664, 245753850, 245753850, 13537664, 166968, 717, 1}
%t Clear[A]; A[1, 1] = 2*4!/4!; A[2, 1] := A[2, 2] = (5)!/4!;
%t A[3, 2] = ( 2*(6)! - 2*4!)/4!; A[4, 2] = A[4, 3] = ( (7)! - 4!)/4!;
%t A[n_, 1] := 1; A[n_, n_] := 1;
%t A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (n + 1)*(n + 2)*A[n - 2, k - 1];
%t a = Table[A[n, k], {n, 10}, {k, n}]; Flatten[a]
%t Table[Apply[Plus, a[[n]]], {n, 1, 10}];
%K nonn,tabl
%O 1,1
%A _Roger L. Bagula_, Dec 31 2008
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