A198793 Triangle T(n,k), read by rows, given by (1,0,0,1,0,0,0,0,0,0,0,...) DELTA (0,1,1,0,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.

1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 6, 4, 0, 1, 4, 12, 16, 8, 0, 1, 5, 20, 40, 40, 16, 0, 1, 6, 30, 80, 120, 96, 32, 0, 1, 7, 42, 140, 280, 336, 224, 64, 0, 1, 8, 56, 224, 560, 896, 896, 512, 128, 0, 1, 9, 72, 336, 1008, 2016, 2688, 2304, 1152, 256, 0

Offset: 0

Author

Philippe Deléham, Oct 30 2011

Keywords

• easy
• nonn
• tabl

Comments

Mirror image of A198792.

Variant of A082137.

Examples

			Triangle begins :
1
1, 0
1, 1, 0
1, 2, 2, 0
1, 3, 6, 4, 0
1, 4, 12, 16, 8, 0,
1, 5, 20, 40, 40, 16, 0
		

Crossrefs

Cf. A082137, A084938, A198792.

Formula

Sum_ {0<=k<=n} T(n,k) = A124302(n).

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

T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) - 2*T(n-2,k-1) for n>2, T(0,0) = T(1,0) = T(2,0) = T(2,1) = 1, T(1,1) = T(2,2) = 0, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Nov 10 2013