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A142465
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Triangle T(n,m) read by rows: T(n,m) = Product_{i=0..5} binomial(n+i,m)/binomial(m+i,m).
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16
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1, 1, 1, 1, 7, 1, 1, 28, 28, 1, 1, 84, 336, 84, 1, 1, 210, 2520, 2520, 210, 1, 1, 462, 13860, 41580, 13860, 462, 1, 1, 924, 60984, 457380, 457380, 60984, 924, 1, 1, 1716, 226512, 3737448, 9343620, 3737448, 226512, 1716, 1, 1, 3003, 736164, 24293412, 133613766, 133613766, 24293412, 736164, 3003, 1
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OFFSET
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0,5
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COMMENTS
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The matrix inverse starts
1;
-1, 1;
6, -7, 1
-141, 168, -28, 1;
9911, -11844, 2016, -84, 1;
-1740901, 2081310, -355320, 15120, -210, 1. - R. J. Mathar, Mar 22 2013
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LINKS
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FORMULA
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T(n,m) = A056941(n,m)*binomial(n+5,m)/binomial(m+5,m).
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, 7, 1;
1, 28, 28, 1;
1, 84, 336, 84, 1;
1, 210, 2520, 2520, 210, 1;
1, 462, 13860, 41580, 13860, 462, 1;
1, 924, 60984, 457380, 457380, 60984, 924, 1;
1, 1716, 226512, 3737448, 9343620, 3737448, 226512, 1716, 1;
1, 3003, 736164, 24293412, 133613766, 133613766, 24293412, 736164, 3003, 1;
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MAPLE
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mul(binomial(n+i, m)/binomial(m+i, m), i=0..5) ;
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MATHEMATICA
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T[n_, k_]:= Product[Binomial[n+j, k]/Binomial[k+j, k], {j, 0, 5}];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
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PROG
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(PARI) T(n, k) = prod(j=0, 5, binomial(n+j, k)/binomial(k+j, k)); \\ Seiichi Manyama, Apr 01 2021
(Magma)
A142465:= func< n, k | (&*[Binomial(n+j, k)/Binomial(k+j, k): j in [0..5]]) >;
(SageMath)
def A142465(n, k): return product(binomial(n+j, k)/binomial(k+j, k) for j in (0..5))
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CROSSREFS
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Triangles of generalized binomial coefficients (n,k)_m (or generalized Pascal triangles) for m = 1,...,12: A007318 (Pascal), A001263, A056939, A056940, A056941, A142465, A142467, A142468, A174109, A342889, A342890, A342891.
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KEYWORD
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AUTHOR
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EXTENSIONS
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Edited by the Associate Editors of the OEIS, May 17 2009
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STATUS
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approved
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