%I #2 Mar 30 2012 17:34:29

%S 2,5,5,2,76,2,2,438,438,2,2,704,10908,704,2,2,1126,103592,103592,1126,

%T 2,2,1740,320142,3545032,320142,1740,2,2,2582,794802,47373814,

%U 47373814,794802,2582,2,2,3688,1757864,224887000,2051605292,224887000,1757864

%N Recursive triangular sequence: A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (3 (-1 + n) (-4 + 3 n))*A(n - 2, k - 1).

%C Row sums are:

%C {2, 10, 80, 880, 12320, 209440, 4188800, 96342400, 2504902400, 72642169600,

%C 2324549427200, 81359229952000}

%F A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (3 (-1 + n) (-4 + 3 n))*A(n - 2, k - 1).

%e {2},

%e {5, 5},

%e {2, 76, 2},

%e {2, 438, 438, 2},

%e {2, 704, 10908, 704, 2},

%e {2, 1126, 103592, 103592, 1126, 2},

%e {2, 1740, 320142, 3545032, 320142, 1740, 2},

%e {2, 2582, 794802, 47373814, 47373814, 794802, 2582, 2},

%e {2, 3688, 1757864, 224887000, 2051605292, 224887000, 1757864, 3688, 2},

%e {2, 5094, 3574116, 784595868, 35532909720, 35532909720, 784595868, 3574116, 5094, 2},

%e {2, 6836, 6787770, 2317511664, 231969195588, 1855962423480, 231969195588, 2317511664, 6787770, 6836, 2},

%e {2, 8950, 12173870, 6098565930, 1062819943860, 39610684283388, 39610684283388, 1062819943860, 6098565930, 12173870, 8950, 2}

%t Clear[A, b, a, f]; f[n_] = N[2*Product[3*k + 5, {k, 0, n - 1}]];

%t A[1, 1] = 2; A[2, 1] := A[2, 2] = 5; A[3, 2] = 80 - 4;

%t A[4, 2] = 880/2 - 2; A[4, 3] = 880/2 - 2; A[n_, 1] := 2; A[n_, n_] := 2;

%t A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (3 (-1 + n) (-4 + 3 n))*A[n - 2,k - 1];

%t a = Table[A[n, k], {n, 12}, {k, n}]; Flatten[a]

%t Table[Apply[Plus, a[[n]]], {n, 1, 12}]; Table[Apply[Plus, a[[n]]]/N[f[n - 1]], {n, 1, 12}];

%K nonn,tabl

%O 1,1

%A _Roger L. Bagula_, Jan 02 2009