A271698 Triangle read by rows, T(n,k) = Sum_{j=0..n} C(-j,-n)*E1(j,k), E1 the Eulerian numbers A173018, for n>=0 and 0<=k<=n.

1, 1, 0, 0, 1, 0, 0, 2, 1, 0, 0, 2, 8, 1, 0, 0, 2, 28, 22, 1, 0, 0, 2, 72, 182, 52, 1, 0, 0, 2, 164, 974, 864, 114, 1, 0, 0, 2, 352, 4174, 8444, 3474, 240, 1, 0, 0, 2, 732, 15782, 61464, 57194, 12660, 494, 1, 0, 0, 2, 1496, 55286, 373940, 660842, 332528, 43358, 1004, 1, 0

Offset: 0

Author

Peter Luschny, Apr 12 2016

Keywords

• nonn
• tabl

Examples

			Triangle starts:
1,
1, 0,
0, 1, 0,
0, 2, 1, 0,
0, 2, 8, 1, 0,
0, 2, 28, 22, 1, 0,
0, 2, 72, 182, 52, 1, 0,
0, 2, 164, 974, 864, 114, 1, 0
		

Links

• Peter Luschny, Extensions of the binomial

Crossrefs

A000255 (row sums), compare A028296 for alternating rows sums, A145654 and A005803 (diag. n,n-2).

Cf. A173018.

Programs

Maple

A271698 := (n,k) -> add(binomial(-j,-n)*combinat:-eulerian1(j,k), j=0..n):
seq(seq(A271698(n, k), k=0..n), n=0..10);

Mathematica

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