_Roger L. Bagula (rlbagulatftn(AT)yahoo.com), _, Dec 27 2008

Recursive triangular symmetrical sequence: A(n,k) := (n - k + 1)A(n - 1, k - 1) + (k)* A(n - 1, k) - (n + 1)*A(n - 2, k - 1).

2, 3, 3, 2, 14, 2, 2, 25, 25, 2, 2, 46, 66, 46, 2, 2, 88, 207, 207, 88, 2, 2, 172, 693, 1128, 693, 172, 2, 2, 340, 2319, 6114, 6114, 2319, 340, 2, 2, 676, 7617, 31440, 49860, 31440, 7617, 676, 2, 2, 1348, 24519, 153570, 370686, 370686, 153570, 24519, 1348, 2

0,1

Row sums are:

{2, 6, 18, 54, 162, 594, 2862, 17550, 129330, 1100250,...}

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

{2},

{3, 3},

{2, 14, 2},

{2, 25, 25, 2},

{2, 46, 66, 46, 2},

{2, 88, 207, 207, 88, 2},

{2, 172, 693, 1128, 693, 172, 2},

{2, 340, 2319, 6114, 6114, 2319, 340, 2},

{2, 676, 7617, 31440, 49860, 31440, 7617, 676, 2},

{2, 1348, 24519, 153570, 370686, 370686, 153570, 24519, 1348, 2}

Clear[t, n, m, A];

A[2, 1] := A[2, 2] = 3;

A[3, 2] = 14; A[4, 2] = 25; A[4, 3] = 25;

A[n_, 1] := 2; A[n_, n_] := 2

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

Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}]

Flatten[%]

nonn,uned,tabl,new

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 27 2008

approved