A202603 Triangle T(n,k), read by rows, given by (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 1, 1, 1, 1, 0, 1, 1, -1, -1, 1, 1, -2, -3, -1, 1, 1, -3, -5, -2, 0, 1, 1, -4, -7, -2, 2, 1, 1, 1, -5, -9, -1, 7, 5, 1, 1, 1, -6, -11, 1, 15, 12, 3, 0, 1, 1, -7, -13, 4, 26, 21, 3, -3, -1, 1, 1, -8, -15, 8, 40, 31, -3, -15, -7, -1

Offset: 0

Author

Philippe Deléham, Dec 21 2011

Keywords

• sign
• tabl

Comments

Mirror image of triangle in A129267.

Examples

			Triangle begins :
1
1, 1
1, 1, 0
1, 1, -1, -1
1, 1, -2, -3, -1
1, 1, -3, -5, -2, 0
1, 1, -4, -7, -2, 2, 1
1, 1, -5, -9, -1, 7, 5, 1
		

Crossrefs

Cf. A129267, A010892, A005449

Formula

T(n,k) = T(n-1,k) + T(n-1,k-1) - T(n-2,k-1) - T(n-2,l-2) with T(0,0)= T(1,0) = T(1,1) = 1 and T(n,k) = 0 if k<0 or if n

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000012(n), A099087(n), A190960(n+1) for x = 0, 1, 2 respectively.

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

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