A199400 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.

1, 2, 2, 4, 10, 6, 8, 38, 54, 24, 16, 130, 330, 336, 120, 32, 422, 1710, 3000, 2400, 720, 64, 1330, 8106, 21840, 29400, 19440, 5040, 128, 4118, 36414, 141624, 285600, 312480, 176400, 40320, 256, 12610, 158010, 853776, 2421720, 3900960, 3598560, 1774080, 362880

Offset

0,2

Comments

Variant of A162508.

Links

Table of n, a(n) for n=0..44.

Formula

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

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

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

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

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

Example

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

Crossrefs

Cf. A084938, A143494, A162508, A162509,

Sequence in context: A240629 A360313 A162508 * A056919 A052175 A102623

Adjacent sequences: A199397 A199398 A199399 * A199401 A199402 A199403

Keyword

nonn,tabl

Author

Philippe Deléham, Nov 05 2011

Status

approved