A271699 Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j,-n)*S1(k,j), S1 the Stirling cycle numbers A132393, for n>=0 and 0<=k<=n.

1, 0, 1, 0, 1, 2, 0, 1, 3, 9, 0, 1, 4, 14, 58, 0, 1, 5, 20, 90, 475, 0, 1, 6, 27, 131, 729, 4666, 0, 1, 7, 35, 182, 1064, 7070, 53116, 0, 1, 8, 44, 244, 1494, 10284, 79470, 684762, 0, 1, 9, 54, 318, 2034, 14478, 114918, 1012368, 9833391

Offset

0,6

Links

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

Example

Triangle starts:
1,
0, 1,
0, 1, 2,
0, 1, 3, 9,
0, 1, 4, 14, 58,
0, 1, 5, 20, 90,  475,
0, 1, 6, 27, 131, 729,  4666,
0, 1, 7, 35, 182, 1064, 7070, 53116

Maple

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

Mathematica

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

Crossrefs

A000027 (col. 2), A000096 (col. 3), A247329 (diag. n,n).

Sequence in context: A153506 A325670 A271701 * A216701 A278326 A018843

Adjacent sequences: A271696 A271697 A271698 * A271700 A271701 A271702

Keyword

nonn,tabl

Author

Peter Luschny, Apr 14 2016

Status

approved