A156141 Triangle T(n,k) = A008517(n,k+1)+A008517(n,n+1-k) read by rows.

2, 1, 1, 1, 4, 1, 1, 14, 14, 1, 1, 46, 116, 46, 1, 1, 172, 772, 772, 172, 1, 1, 834, 5160, 8800, 5160, 834, 1, 1, 5280, 39594, 90260, 90260, 39594, 5280, 1, 1, 40814, 361086, 981104, 1288040, 981104, 361086, 40814, 1, 1, 363884, 3801180, 12088796

Offset: 0

Author

Roger L. Bagula, Feb 04 2009

Keywords

• nonn
• tabl

Comments

Row sums are 2*A001147(n).

Examples

			{2},
{1, 1},
{1, 4, 1},
{1, 14, 14, 1},
{1, 46, 116, 46, 1},
{1, 172, 772, 772, 172, 1},
{1, 834, 5160, 8800, 5160, 834, 1},
{1, 5280, 39594, 90260, 90260, 39594, 5280, 1},
{1, 40814, 361086, 981104, 1288040, 981104, 361086, 40814, 1},
{1, 363884, 3801180, 12088796, 18205564, 18205564, 12088796, 3801180, 363884, 1},
{1, 3630826, 44557888, 167513072, 283669904, 310714768, 283669904, 167513072, 44557888, 3630826, 1}
		

Links

• E. W. Weisstein, Second-Order Eulerian Triangle

Crossrefs

Cf. A008517

Programs

Mathematica

e[n_, 0] := 1;
e[n_, k_] := 0 /; k >= n;
e[n_, k_] := (k + 1)e[n - 1, k] + (2n - k - 1)e[n - 1, k - 1];
Table[Table[e[n, k] + e[n, n - k], {k, 0, n}], {n, 0, 10}];
Flatten[%]

Formula

T(n,0)=T(n,n) =1, n>=1.

T(n,k)= A008517(n,k+1)+A008517(n,n+1-k), n>1, 0

T(n,k)= T(n,n-k) .

Extensions

Definition simplified by the Associate Editors of the OEIS Sep 17 2009

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.