A171616 Triangle T : T(n,k)= binomial(n,k)*A000957(n+1-k).

1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 6, 8, 6, 0, 1, 18, 30, 20, 10, 0, 1, 57, 108, 90, 40, 15, 0, 1, 186, 399, 378, 210, 70, 21, 0, 1, 622, 1488, 1596, 1008, 420, 112, 28, 0, 1, 2120, 5598, 6696, 4788, 2268, 756, 168, 36, 0, 1, 7338, 21200, 27990, 22320, 11970, 4536, 1260, 240, 45

Offset

0,7

Links

Table of n, a(n) for n=0..63.

Formula

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000957(n+1), A033321(n), A033543(n) for x = 0,1,2 respectively. Sum_{k, 0<=k<=n} T(n,k)*(-1)^(n-k)*x^k = A054341(n), A059738(n), A049027(n+1) for x = 2,3,4 respectively.

Example

Triangle begins : 1 ; 0,1 ; 1,0,1 ; 2,3,0,1 ; 6,8,6,0,1 ; 18,30,20,10,0,1 ; ...

Crossrefs

Cf. A007318

Sequence in context: A366258 A319665 A004443 * A323883 A008290 A322147

Adjacent sequences: A171613 A171614 A171615 * A171617 A171618 A171619

Keyword

nonn,tabl

Author

Philippe Deléham, Dec 13 2009

Status

approved