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

0,8

Links

Table of n, a(n) for n=0..65.

Peter Luschny, Extensions of the binomial

Example

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

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

<<Combinatorica`
Flatten[Table[Sum[Binomial[-j, -n]  Eulerian[j, k], {j, 0, n}], {n, 0, 9}, {k, 0, n}]]

Crossrefs

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

Cf. A173018.

Sequence in context: A301503 A059431 A289358 * A113263 A063658 A237053

Adjacent sequences: A271695 A271696 A271697 * A271699 A271700 A271701

Keyword

nonn,tabl

Author

Peter Luschny, Apr 12 2016

Status

approved