A269954 Triangle read by rows, T(n,k) = Sum_{j=0..n} C(-j,-n)*S1(j,k), S1 the Stirling cycle numbers A132393, for n>=0 and 0<=k<=n.

1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 2, 5, 3, 1, 0, 9, 20, 17, 6, 1, 0, 44, 109, 100, 45, 10, 1, 0, 265, 689, 694, 355, 100, 15, 1, 0, 1854, 5053, 5453, 3094, 1015, 196, 21, 1, 0, 14833, 42048, 48082, 29596, 10899, 2492, 350, 28, 1

Offset

0,12

Links

Table of n, a(n) for n=0..54.

Peter Luschny, Extensions of the binomial

Example

Triangle starts:
1,
0,   1,
0,   0,   1,
0,   1,   1,  1,
0,   2,   5,  3,    1,
0,   9,  20,  17,   6,   1,
0,  44, 109, 100,  45,  10,  1,
0, 265, 689, 694, 355, 100, 15, 1.

Maple

A269954 := (n, k) -> add(binomial(-j, -n)*abs(Stirling1(j, k)), j=0..n):
seq(seq(A269954(n, k), k=0..n), n=0..9);

Mathematica

Flatten[Table[Sum[Binomial[-j, -n] Abs[StirlingS1[j, k]], {j, 0, n}], {n, 0, 9}, {k, 0, n}]]

Crossrefs

A000255 (row sums), A000166(col. 1), A000217 (diag. n,n-1), A133252 (diag. n,n-2).

Sequence in context: A365728 A265318 A279536 * A326953 A234255 A062706

Adjacent sequences: A269951 A269952 A269953 * A269955 A269956 A269957

Keyword

nonn,tabl

Author

Peter Luschny, Apr 12 2016

Status

approved