A206831 Triangle T(n,k), read by rows, given by (1, -2, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 1, 1, -1, 0, 1, -1, -3, -1, 1, 1, 0, -4, -2, 1, 1, 5, 4, -4, -3, 1, -1, 0, 9, 10, -3, -4, 1, -1, -7, -9, 9, 17, -1, -5, 1, 1, 0, -16, -28, 2, 24, 2, -6, 1, 1, 9, 16, -16, -54, -14, 30, 6, -7, 1, -1, 0, 25, 60, 10

Offset: 0

Author

Philippe Deléham, Feb 13 2012

Keywords

• easy
• sign
• tabl

Comments

Riordan array ((1+x)/(1+x^2), x*(1-x)/(1+x^2)).

Antidiagonal sums are A010892(n).

Examples

			Triangle begins :
1
1, 1
-1, 0, 1
-1, -3, -1, 1
1, 0, -4, -2, 1
1, 5, 4, -4, -3, 1
-1, 0, 9, 10, -3, -4, 1
-1, -7, -9, 9, 17, -1, -5, 1
1, 0, -16, -28, 2, 24, 2, -6, 1
1, 9, 16, -16, -54, -14, 30, 6, -7, 1
-1, 0, 25, 60, 10, -80, -40, 34, 11, -8, 1
		

Links

• Indranil Ghosh, Rows 0..100, flattened

Crossrefs

Cf. A129267, A007318, A147703, A147721

Cf. A057077, A087960

Programs

Mathematica

nmax=10; Flatten[CoefficientList[Series[CoefficientList[Series[(1 + x)/(1 - y*x + (1 + y)*x^2), {x, 0, nmax}], x], {y, 0, nmax}], y]] (* Indranil Ghosh, Mar 10 2017 *)

Formula

T(n,k) = T(n-1,k-1) - T(n-2,k) - T(n-2,k-1), n>1.

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

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A057077(n), (-1)^n*A078050(n) for x = -1, 0, 1 respectively.