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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, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Mirror image of triangle in A198321.
Variant of A074909, A135278.
LINKS
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
Sequence in context: A208727 A242378 A268820 * A206735 A089000 A253829
KEYWORD
easy,nonn,tabl
AUTHOR
Philippe Deléham, Nov 01 2011
STATUS
approved

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Last modified May 21 05:29 EDT 2024. Contains 372726 sequences. (Running on oeis4.)