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Search: id:A130777
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| 1, -1, 1, -1, -1, 1, 1, -2, -1, 1, 1, 2, -3, -1, 1, -1, 3, 3, -4, -1, 1, -1, -3, 6, 4, -5, -1, 1, 1, -4, -6, 10, 5, -6, -1, 1, 1, 4, -10, -10, 15, 6, -7, -1, 1, -1, 5, 10, -20, -15, 21, 7, -8, -1, 1, -1, -5, 15, 20, -35, -21, 28, 8, -9, -1, 1, 1, -6, -15, 35, 35, -56, -28, 36, 9, -10, -1, 1
(list; table; graph; listen)
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OFFSET
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0,8
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COMMENT
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Signed version of A046854.
Contribution from Paul Barry (pbarry(AT)wit.ie), May 21 2009: (Start)
Riordan array ((1-x)/(1+x^2),x/(1+x^2)).
This triangle is the coefficient triangle for the Hankel transforms of the family of generalized Catalan numbers
that satisfy a(n;r)=r*a(n-1;r)+sum{k=1..n-2, a(k)*a(n-1-k;r)}, a(0;r)=a(1;r)=1. The Hankel transform of
a(n;r) is h(n)=sum{k=0..n, T(n,k)*r^k} with g.f. (1-x)/(1-rx+x^2). These sequences include A086246, A000108, A002212. (End)
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FORMULA
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Number triangle T(n,k)=(-1)^C(n-k+1,2)*C(floor((n+k)/2),k). [From Paul Barry (pbarry(AT)wit.ie), May 21 2009]
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EXAMPLE
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Triangle begins:
1;
-1, 1;
-1, -1, 1;
1, -2, -1, 1;
1, 2, -3, -1, 1;
-1, 3, 3, -4, -1, 1;
-1, -3, 6, 4, -5, -1, 1;
1, -4, -6, 10, 5, -6, -1, 1;
1, 4, -10, -10, 15, 6, -7, -1, 1 ;...
Contribution from Paul Barry (pbarry(AT)wit.ie), May 21 2009: (Start)
Production matrix is
-1, 1,
-2, 0, 1,
-2, -1, 0, 1,
-4, 0, -1, 0, 1,
-6, -1, 0, -1, 0, 1,
-12, 0, -1, 0, -1, 0, 1,
-20, -2, 0, -1, 0, -1, 0, 1,
-40, 0, -2, 0, -1, 0, -1, 0, 1,
-70, -5, 0, -2, 0, -1, 0, -1, 0, 1 (End)
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CROSSREFS
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Cf. A066170 A046854.
Sequence in context: A144406 A096670 A130461 this_sequence A046854 A066170 A071773
Adjacent sequences: A130774 A130775 A130776 this_sequence A130778 A130779 A130780
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KEYWORD
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sign,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 14 2007
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