A201093 Triangle T(n,k), read by rows, given by (0,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,...) DELTA (1,0,0,0,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.

1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 3, 1, 0, 0, 2, 3, 4, 1, 0, 2, 2, 4, 6, 5, 1, 0, 0, 4, 6, 8, 10, 6, 1, 0, 5, 5, 9, 13, 15, 15, 7, 1, 0, 0, 10, 15, 20, 25, 26, 21, 8, 1, 0, 14, 14, 24, 34, 41, 45, 42, 28, 9, 1

Offset: 0

Author

Philippe Deléham, Nov 26 2011

Keywords

• nonn
• tabl

Comments

Riordan array (1,xf(x)) where f(x) is g.f. of A097331.

Row sums are in A001405.

Examples

			Triangle begins :
1
0, 1
0, 1, 1
0, 0, 2, 1
0, 1, 1, 3, 1
0, 0, 2, 3, 4, 1
0, 2, 2, 4, 6, 5, 1
0, 0, 4, 6, 8, 10, 6, 1
0, 5, 5, 9, 13, 15, 15, 7, 1
0, 0, 10, 15, 20, 25, 26, 21, 8, 1
0, 14, 14, 24, 34, 41, 45, 42, 28, 9, 1
0, 0, 28, 42, 56, 70, 78, 77, 64, 36, 10, 1
0, 42, 42, 70, 98, 120, 136, 140, 126, 93, 45, 11, 1
		

Crossrefs

Cf. Diagonals : A000012, A001477, A000217, A000215,

Columns :A000007, A097331, A089408

Formula

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A001405(n), A098617(n) for x = 0,1,2 respectively.