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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.
2
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
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).
Sequence in context: A030206 A212768 A133336 * A176056 A373224 A298213
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Apr 10 2016
STATUS
approved