A271701 Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j,-n)*S2(k,j), S2 the Stirling set numbers A048993, for n>=0 and 0<=k<=n.

1, 0, 1, 0, 1, 2, 0, 1, 3, 8, 0, 1, 4, 13, 41, 0, 1, 5, 19, 69, 252, 0, 1, 6, 26, 106, 431, 1782, 0, 1, 7, 34, 153, 681, 3068, 14121, 0, 1, 8, 43, 211, 1016, 4929, 24361, 123244, 0, 1, 9, 53, 281, 1451, 7515, 39537, 212509, 1169832

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, 8]
[0, 1, 4, 13, 41]
[0, 1, 5, 19, 69,  252]
[0, 1, 6, 26, 106, 431, 1782]
[0, 1, 7, 34, 153, 681, 3068, 14121]

Maple

T := (n, k) -> add(Stirling2(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] StirlingS2[k, j], {j, 0, n}], {n, 0, 9}, {k, 0, n}]]

Crossrefs

Sequence in context: A325842 A153506 A325670 * A271699 A216701 A278326

Adjacent sequences: A271698 A271699 A271700 * A271702 A271703 A271704

Keyword

nonn,tabl

Author

Peter Luschny, Apr 14 2016

Status

approved