A199011 Triangle T(n,k), read by rows, given by (1,1,-1,1,0,0,0,0,0,0,0,...) DELTA (0,1,0,0,0,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.

1, 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

Offset

0,4

Comments

Mirror image of triangle in A198321.

Variant of A074909, A135278.

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k)=binomial(n,k+1).

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

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

T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - T(n-2,k) - T(n-2,k-1), T(0,0) = T(1,0) = T(2,1) = 1, T(1,1) = T(2,2) = 0, T(2,0) = 2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Feb 12 2014

Example

Triangle begins :
1
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

Crossrefs

Cf. A007318, A074909, A135278, A198321

Sequence in context: A208727 A242378 A268820 * A206735 A089000 A253829

Adjacent sequences: A199008 A199009 A199010 * A199012 A199013 A199014

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Nov 01 2011

Status

approved