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A079508
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Triangle T(n,k) (n >= 2, k >= 1) of Raney numbers read by rows.
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2
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1, 0, 1, 0, 2, 1, 0, 0, 5, 1, 0, 0, 5, 9, 1, 0, 0, 0, 21, 14, 1, 0, 0, 0, 14, 56, 20, 1, 0, 0, 0, 0, 84, 120, 27, 1, 0, 0, 0, 0, 42, 300, 225, 35, 1, 0, 0, 0, 0, 0, 330, 825, 385, 44, 1, 0, 0, 0, 0, 0, 132, 1485, 1925, 616, 54, 1
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OFFSET
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2,5
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COMMENTS
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There are only m nonzero entries in the m-th column.
Related to A033282: shift row n of A033282 triangle n places to the right and transpose the resulting table. - Michel Marcus, Feb 04 2014
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LINKS
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FORMULA
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EXAMPLE
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Triangle starts:
1;
0, 1;
0, 2, 1;
0, 0, 5, 1;
0, 0, 5, 9, 1;
0, 0, 0, 21, 14, 1;
0, 0, 0, 14, 56, 20, 1;
0, 0, 0, 0, 84, 120, 27, 1;
0, 0, 0, 0, 42, 300, 225, 35, 1;
0, 0, 0, 0, 0, 330, 825, 385, 44, 1;
0, 0, 0, 0, 0, 132, 1485, 1925, 616, 54, 1;
... (End)
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MATHEMATICA
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Table[Binomial[k, n-k]*Binomial[n, k+1]/k, {n, 2, 10}, {k, 1, n-1}]//Flatten (* G. C. Greubel, Jan 17 2019 *)
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PROG
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(PARI) tabl(nn) = {for (n = 2, nn, for (k = 1, n-1, print1(binomial(k, n-k)*binomial(n, k+1)/k, ", "); ); print(); ); } \\ Michel Marcus, Feb 04 2014
(Magma) [[Binomial(k, n-k)*Binomial(n, k+1)/k: k in [1..n-1]]: n in [2..10]]; // G. C. Greubel, Jan 17 2019
(Sage) [[binomial(k, n-k)*binomial(n, k+1)/k for k in (1..n-1)] for n in (2..10)] # G. C. Greubel, Jan 17 2019
(GAP) Flat(List([1..10], n->List([1..n-1], k-> Binomial(k, n-k)*Binomial(n , k+1)/k ))); # G. C. Greubel, Jan 17 2019
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CROSSREFS
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Sum of nonzero entries in each column gives A001003. Alternating sum of each column is 1. Second diagonal on right gives A000096.
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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