|
| |
|
|
A269952
|
|
Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j,-n)*S2(j,k), S2 the Stirling set numbers A048993, for n>=0 and 0<=k<=n.
|
|
2
|
|
|
|
1, 0, 1, 0, 2, 1, 0, 4, 5, 1, 0, 8, 19, 9, 1, 0, 16, 65, 55, 14, 1, 0, 32, 211, 285, 125, 20, 1, 0, 64, 665, 1351, 910, 245, 27, 1, 0, 128, 2059, 6069, 5901, 2380, 434, 35, 1, 0, 256, 6305, 26335, 35574, 20181, 5418, 714, 44, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,5
|
|
|
LINKS
|
Table of n, a(n) for n=0..54.
Peter Luschny, Extensions of the binomial
|
|
|
FORMULA
|
T(n, k) = S2(n+1, k+1) - S2(n, k+1).
|
|
|
EXAMPLE
|
1,
0, 1,
0, 2, 1,
0, 4, 5, 1,
0, 8, 19, 9, 1,
0, 16, 65, 55, 14, 1,
0, 32, 211, 285, 125, 20, 1,
0, 64, 665, 1351, 910, 245, 27, 1.
|
|
|
MAPLE
|
A269952 := (n, k) -> Stirling2(n+1, k+1) - Stirling2(n, k+1):
seq(seq(A269952(n, k), k=0..n), n=0..9);
|
|
|
MATHEMATICA
|
Flatten[ Table[ Sum[(-1)^(n-j) Binomial[-j, -n] StirlingS2[j, k], {j, 0, n}], {n, 0, 9}, {k, 0, n}]]
|
|
|
CROSSREFS
|
Variant: A143494 (the main entry for this triangle).
A005493 (row sums), A074051 (alt. row sums), A000079 (col. 1), A001047 (col. 2),
A016269 (col. 3), A025211 (col. 4), A000096 (diag. n,n-1), A215862 (diag. n,n-2),
A049444, A136124, A143491 (matrix inverse).
Cf. A048993, A269951.
Sequence in context: A100887 A073592 A164994 * A247268 A266867 A151852
Adjacent sequences: A269949 A269950 A269951 * A269953 A269954 A269955
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
Peter Luschny, Apr 10 2016
|
|
|
STATUS
|
approved
|
| |
|
|
