A153759 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).

2, 5, 5, 1, 58, 1, 1, 209, 209, 1, 1, 252, 2854, 252, 1, 1, 309, 14810, 14810, 309, 1, 1, 382, 33263, 235108, 33263, 382, 1, 1, 473, 61455, 1601271, 1601271, 61455, 473, 1, 1, 584, 103948, 5321656, 29064422, 5321656, 103948, 584, 1, 1, 717, 166968, 13537664

Offset

1,1

Comments

Row sums are:(2*(n + 3)!)/4!:

{2, 10, 60, 420, 3360, 30240, 302400, 3326400, 39916800, 518918400,...}

Links

Table of n, a(n) for n=1..49.

Formula

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

Example

{2},
{5, 5},
{1, 58, 1},
{1, 209, 209, 1},
{1, 252, 2854, 252, 1},
{1, 309, 14810, 14810, 309, 1},
{1, 382, 33263, 235108, 33263, 382, 1},
{1, 473, 61455, 1601271, 1601271, 61455, 473, 1},
{1, 584, 103948, 5321656, 29064422, 5321656, 103948, 584, 1},
{1, 717, 166968, 13537664, 245753850, 245753850, 13537664, 166968, 717, 1}

Mathematica

Clear[A]; A[1, 1] = 2*4!/4!; A[2, 1] := A[2, 2] = (5)!/4!;
A[3, 2] = ( 2*(6)! - 2*4!)/4!; A[4, 2] = A[4, 3] = ( (7)! - 4!)/4!;
A[n_, 1] := 1; A[n_, n_] := 1;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (n + 1)*(n + 2)*A[n - 2, k - 1];
a = Table[A[n, k], {n, 10}, {k, n}]; Flatten[a]
Table[Apply[Plus, a[[n]]], {n, 1, 10}];

Crossrefs

Sequence in context: A340422 A145428 A086283 * A269992 A146100 A101458

Adjacent sequences: A153756 A153757 A153758 * A153760 A153761 A153762

Keyword

nonn,tabl

Author

Roger L. Bagula, Dec 31 2008

Status

approved