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Triangle T(n,k), read by rows, given by (2,0,3,0,4,0,5,0,6,0,7,0,8,0,9,...) DELTA (2,1,3,2,4,3,5,4,6,5,7,6,8,7,9,...) where DELTA is the operator defined in A084938.
2

%I #10 Jul 21 2014 09:14:14

%S 1,2,2,4,10,6,8,38,54,24,16,130,330,336,120,32,422,1710,3000,2400,720,

%T 64,1330,8106,21840,29400,19440,5040,128,4118,36414,141624,285600,

%U 312480,176400,40320,256,12610,158010,853776,2421720,3900960,3598560,1774080,362880

%N Triangle T(n,k), read by rows, given by (2,0,3,0,4,0,5,0,6,0,7,0,8,0,9,...) DELTA (2,1,3,2,4,3,5,4,6,5,7,6,8,7,9,...) where DELTA is the operator defined in A084938.

%C Variant of A162508.

%F T(n,k)=(k+1)!*A143494(n+2,k+2)

%F T(n,k)=(k+1)*T(n-1,k-1)+(k+2)*T(n-1,k).

%F Sum_{k, 0<=k<=n} T(n,k)=A162509(n+1).

%F T(n,n)=(n+1)!=A000142(n+1)

%F T(n,0)=2^n=A000079(n).

%e Triangle begins :

%e 1

%e 2, 2

%e 4, 10, 6

%e 8, 38, 54, 24

%e 16, 130, 330, 336, 120

%e 32, 422, 1710, 3000, 2400, 720

%Y Cf. A084938, A143494, A162508, A162509,

%K nonn,tabl

%O 0,2

%A _Philippe Deléham_, Nov 05 2011