A269951 Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j,-n)*S1(j,k), S1 the Stirling cycle numbers A132393, for n>=0 and 0<=k<=n.

1, 0, 1, 0, 2, 1, 0, 5, 5, 1, 0, 16, 23, 9, 1, 0, 65, 116, 65, 14, 1, 0, 326, 669, 470, 145, 20, 1, 0, 1957, 4429, 3634, 1415, 280, 27, 1, 0, 13700, 33375, 30681, 14084, 3535, 490, 35, 1, 0, 109601, 283072, 284066, 147532, 43939, 7756, 798, 44, 1

Offset

0,5

Links

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

Peter Luschny, Extensions of the binomial

Example

1,
0, 1,
0, 2,   1,
0, 5,   5,   1,
0, 16,  23,  9,   1,
0, 65,  116, 65,  14,  1,
0, 326, 669, 470, 145, 20, 1.

Maple

A269951 := (n, k) -> add((-1)^(n-j)*binomial(-j, -n)*abs(Stirling1(j, k)), j=0..n):
seq(seq(A269951(n, k), k=0..n), n=0..9);

Mathematica

Flatten[ Table[ Sum[(-1)^(n-j) Binomial[-j, -n] Abs[StirlingS1[j, k]], {j, 0, n}], {n, 0, 9}, {k, 0, n}]]

Crossrefs

A000522 (col. 1), A073596 (col. 2), A000096 (diag. n-1), A241765 (diag. n-2).

A001339 (row sums), A137597 (unsigned matrix inverse).

Cf. A132393, A269952.

Sequence in context: A030206 A212768 A133336 * A176056 A373224 A298213

Adjacent sequences: A269948 A269949 A269950 * A269952 A269953 A269954

Keyword

nonn,tabl

Author

Peter Luschny, Apr 10 2016

Status

approved