A153821 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).

2, 5, 5, 2, 76, 2, 2, 438, 438, 2, 2, 704, 10908, 704, 2, 2, 1126, 103592, 103592, 1126, 2, 2, 1740, 320142, 3545032, 320142, 1740, 2, 2, 2582, 794802, 47373814, 47373814, 794802, 2582, 2, 2, 3688, 1757864, 224887000, 2051605292, 224887000, 1757864

Offset

1,1

Comments

Row sums are:

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

2324549427200, 81359229952000}

Links

Table of n, a(n) for n=1..43.

Formula

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

Example

{2},
{5, 5},
{2, 76, 2},
{2, 438, 438, 2},
{2, 704, 10908, 704, 2},
{2, 1126, 103592, 103592, 1126, 2},
{2, 1740, 320142, 3545032, 320142, 1740, 2},
{2, 2582, 794802, 47373814, 47373814, 794802, 2582, 2},
{2, 3688, 1757864, 224887000, 2051605292, 224887000, 1757864, 3688, 2},
{2, 5094, 3574116, 784595868, 35532909720, 35532909720, 784595868, 3574116, 5094, 2},
{2, 6836, 6787770, 2317511664, 231969195588, 1855962423480, 231969195588, 2317511664, 6787770, 6836, 2},
{2, 8950, 12173870, 6098565930, 1062819943860, 39610684283388, 39610684283388, 1062819943860, 6098565930, 12173870, 8950, 2}

Mathematica

Clear[A, b, a, f]; f[n_] = N[2*Product[3*k + 5, {k, 0, n - 1}]];
A[1, 1] = 2; A[2, 1] := A[2, 2] = 5; A[3, 2] = 80 - 4;
A[4, 2] = 880/2 - 2; A[4, 3] = 880/2 - 2; A[n_, 1] := 2; A[n_, n_] := 2;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (3 (-1 + n) (-4 + 3 n))*A[n - 2, k - 1];
a = Table[A[n, k], {n, 12}, {k, n}]; Flatten[a]
Table[Apply[Plus, a[[n]]], {n, 1, 12}]; Table[Apply[Plus, a[[n]]]/N[f[n - 1]], {n, 1, 12}];

Crossrefs

Sequence in context: A153518 A153648 A153354 * A153879 A074250 A161013

Adjacent sequences: A153818 A153819 A153820 * A153822 A153823 A153824

Keyword

nonn,tabl

Author

Roger L. Bagula, Jan 02 2009

Status

approved