A202992 Triangle T(n,k), read by rows, given by (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...) DELTA (0, 0, 1, 1, 2, 2, 3, 3, 4, 4, ...) where DELTA is the operator defined in A084938.

1, 1, 0, 2, 0, 0, 5, 1, 0, 0, 14, 8, 2, 0, 0, 42, 46, 26, 6, 0, 0, 132, 232, 220, 112, 24, 0, 0, 429, 1093, 1527, 1275, 596, 120, 0, 0, 1430, 4944, 9436, 11384, 8638, 3768, 720, 0, 0, 4862, 21778, 54004, 87556, 95126, 66938, 27576, 5040, 0, 0

Offset

0,4

Comments

T(n,0) = A000108(n) (the Catalan numbers).

Row sums are the factorials (A000142).

Links

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

Formula

T(n,0) = A000108(n), Catalan numbers. Row sums = n! = A000142(n).

T(n+2,n) = n!, n>0.

Sum_{k, 0<=k<=n} T(n,k)*x^k = A011782(n), A000108(n), A000142(n) for x = -1, 0, 1 respectively.

Example

Triangle begins :
1
1, 0
2, 0, 0
5, 1, 0, 0
14, 8, 2, 0, 0
42, 46, 26, 6, 0, 0
132, 232, 220, 112, 24, 0, 0

Crossrefs

Cf. A000108, A000142, A011782, A145879

Sequence in context: A259701 A147843 A094597 * A158830 A275744 A290321

Adjacent sequences: A202989 A202990 A202991 * A202993 A202994 A202995

Keyword

nonn,tabl

Author

Philippe Deléham, Dec 26 2011

Status

approved