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Search: id:A053538
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| A053538 |
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Triangle: a(n,m) = ways to place p balls in n slots with m in the rightmost p slots, 0<=p<=n, 0<=m<=n, summed over p, a(n,m)= Sum[binomial[k,m]binomial[n-k,k-m],{k,0,n} ], (see program line). |
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3
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| 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 5, 4, 1, 1, 8, 10, 7, 5, 1, 1, 13, 18, 16, 9, 6, 1, 1, 21, 33, 31, 23, 11, 7, 1, 1, 34, 59, 62, 47, 31, 13, 8, 1, 1, 55, 105, 119, 101, 66, 40, 15, 9, 1, 1, 89, 185, 227, 205, 151, 88, 50, 17, 10, 1, 1, 144, 324, 426, 414, 321, 213, 113, 61, 19, 11
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Riordan array (1/(1-x-x^2), x(1-x)/(1-x-x^2)). Row sums are A000079. Diagonal sums are A006053(n+2). - Paul Barry (pbarry(AT)wit.ie), Nov 01 2006
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EXAMPLE
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n=4; Table[binomial[k, j]binomial[n-k, k-j], {k, 0, n}, {j, 0, n}] splits {1, 4, 6, 4, 1} into {{1, 0, 0, 0, 0}, {3, 1, 0, 0, 0}, {1, 4, 1, 0, 0}, {0, 0, 3, 1, 0}, {0, 0, 0, 0, 1}} and this gives summed by columns {5, 5, 4, 1, 1}
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MATHEMATICA
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Table[Sum[Binomial[k, m]Binomial[n-k, k-m], {k, 0, n} ], {n, 0, 4}, {m, 0, n} ]
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CROSSREFS
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Sequence in context: A157219 A167040 A054450 this_sequence A138201 A154221 A026736
Adjacent sequences: A053535 A053536 A053537 this_sequence A053539 A053540 A053541
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KEYWORD
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nonn,tabl
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 23 2001
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