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

0,1

Comments

Row sums are 2*A001147(n).

Links

Table of n, a(n) for n=0..48.

E. W. Weisstein, Second-Order Eulerian Triangle

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<k<n.

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

Example

{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}

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[%]

Crossrefs

Cf. A008517

Sequence in context: A260757 A157114 A156786 * A174555 A157113 A214712

Adjacent sequences: A156138 A156139 A156140 * A156142 A156143 A156144

Keyword

nonn,tabl

Author

Roger L. Bagula, Feb 04 2009

Extensions

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

Status

approved