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

0,5

Comments

A103452*A007318 as infinite lower triangular matrices.

Essentially the same as A199011.

Links

Table of n, a(n) for n=0..77.

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.

Example

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).

Sequence in context: A242378 A268820 A199011 * A089000 A253829 A107238

Adjacent sequences: A206732 A206733 A206734 * A206736 A206737 A206738

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Feb 11 2012

Status

approved