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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.
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%I #9 Feb 22 2013 14:40:24

%S 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,

%T 429,1093,1527,1275,596,120,0,0,1430,4944,9436,11384,8638,3768,720,0,

%U 0,4862,21778,54004,87556,95126,66938,27576,5040,0,0

%N 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.

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

%C Row sums are the factorials (A000142).

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

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

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

%e Triangle begins :

%e 1

%e 1, 0

%e 2, 0, 0

%e 5, 1, 0, 0

%e 14, 8, 2, 0, 0

%e 42, 46, 26, 6, 0, 0

%e 132, 232, 220, 112, 24, 0, 0

%Y Cf. A000108, A000142, A011782, A145879

%K nonn,tabl

%O 0,4

%A _Philippe Deléham_, Dec 26 2011