A206735 Triangle T(n,k), read by rows, given by (0, 2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 6, 4, 1, 0, 5, 10, 10, 5, 1, 0, 6, 15, 20, 15, 6, 1, 0, 7, 21, 35, 35, 21, 7, 1, 0, 8, 28, 56, 70, 56, 28, 8, 1, 0, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 0, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1

Offset: 0

Author

Philippe Deléham, Feb 11 2012

Keywords

• easy
• nonn
• tabl

Comments

A103452*A007318 as infinite lower triangular matrices.

Essentially the same as A199011.

Examples

			Triangle begins :
1
0, 1
0, 2, 1
0, 3, 3, 1
0, 4, 6, 4, 1
0, 5, 10, 10, 5, 1
0, 6, 15, 20, 15, 6, 1
0, 7, 21, 35, 35, 21, 7, 1
0, 8, 28, 56, 70, 56, 28, 8, 1
0, 9, 36, 84, 126, 126, 84, 36, 9, 1
0, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1
0, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1
		

Crossrefs

Cf. A007318, A000071 (antidiagonal sums).

Formula

T(n,k) = A007318(n,k) - A073424(n,k).

Sum_{k, 0<=k<=n} T(n,k)*x^k = (1+x)^n - 1 + 0^n.

T(n,0) = 0^n = A000007(n), T(n,k) = binomial(n,k) for k>0.

G.f.: (1-2*x+(1+y)*x^2)/(1-2x+(1+y)*x^2-y*x).

Sum{k, 0<=k<=n} T(n,k)^x = A000027(n+1), A000225(n), A030662(n), A096191(n), A096192(n) for x = 0, 1, 2, 3, 4 respectively.