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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
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
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
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Apr 12 2016
STATUS
approved