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A206831
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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.
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0
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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
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OFFSET
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0,8
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COMMENTS
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Riordan array ((1+x)/(1+x^2), x*(1-x)/(1+x^2)).
Antidiagonal sums are A010892(n).
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LINKS
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Table of n, a(n) for n=0..59.
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FORMULA
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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.
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EXAMPLE
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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
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CROSSREFS
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Cf. A129267, A007318, A147703, A147721
Cf. A057077, A087960
Sequence in context: A104608 A110245 A136093 * A134108 A176851 A205535
Adjacent sequences: A206828 A206829 A206830 * A206832 A206833 A206834
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Philippe Deléham, Feb 13 2012
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STATUS
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approved
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