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A104597
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Triangle T read by rows: inverse of Motzkin triangle A097609.
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2
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1, 0, 1, -1, 0, 1, -1, -2, 0, 1, 0, -2, -3, 0, 1, 1, 1, -3, -4, 0, 1, 1, 4, 3, -4, -5, 0, 1, 0, 3, 9, 6, -5, -6, 0, 1, -1, -2, 5, 16, 10, -6, -7, 0, 1, -1, -6, -9, 6, 25, 15, -7, -8, 0, 1, 0, -4, -18, -24, 5, 36, 21, -8, -9, 0, 1, 1, 3, -7, -39, -50, 1, 49, 28, -9, -10, 0, 1, 1, 8
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| Riordan array ((1-x)/(1-x+x^2),x(1-x)/(1-x+x^2)). - Paul Barry (pbarry(AT)wit.ie), Jun 21 2008
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LINKS
| D. Merlini, R. Sprugnoli and M. C. Verri, An algebra for proper generating trees
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FORMULA
| T(n,m)=sum(j=0..m, binomial(m,j)*sum(k=0..n, binomial(k,n-k)*(-1)^(n-k)*binomial(k+j-1,j-1))*(-1)^(m-j)). [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Apr 08 2011]
T(n,m)=sum(k=ceiling((n-m-1)/2)..n-m, binomial(k+m,m)*binomial(k+1,n-k-m)*(-1)^(n-k-m)). [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Dec 17 2011]
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EXAMPLE
| 1
0,1
-1,0,1
-1,-2,0,1
0,-2,-3,0,1
1,1,-3,-4,0,1
1,4,3,-4,-5,0,1
0,3,9,6,-5,-6,0,1
-1,-2,5,16,10,-6,-7,0,1
-1,-6,-9,6,25,15,-7,-8,0,1
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PROG
| (Maxima)
T(n, m):=sum(binomial(m, j)*sum(binomial(k, n-k)*(-1)^(n-k)*binomial(k+j-1, j-1), k, 0, n)*(-1)^(m-j), j, 0, m); [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Apr 08 2011]
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CROSSREFS
| Row sums are A009116 with different signs.
Sequence in context: A029397 A125079 A129447 * A182936 A072662 A030010
Adjacent sequences: A104594 A104595 A104596 * A104598 A104599 A104600
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KEYWORD
| sign,tabl
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AUTHOR
| Ralf Stephan, Mar 17 2005
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