The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A316674

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A316674

Number A(n,k) of paths from {0}^k to {n}^k that always move closer to {n}^k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
(history; published version)

#27 by Joerg Arndt at Thu Nov 04 06:01:56 EDT 2021

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reviewed

approved

#26 by Michel Marcus at Thu Nov 04 05:43:09 EDT 2021

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proposed

reviewed

#25 by Jean-François Alcover at Thu Nov 04 05:14:16 EDT 2021

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editing

proposed

#24 by Jean-François Alcover at Thu Nov 04 05:14:12 EDT 2021

MATHEMATICA

A[n_, k_] := Sum[If[k == 0, 1, Binomial[j+n-1, n]^k] Sum[(-1)^(i-j)* Binomial[i, j], {i, j, n k}], {j, 0, n k}];

Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 10}] // Flatten (* Jean-François Alcover, Nov 04 2021 *)

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approved

editing

#23 by Alois P. Heinz at Fri Jan 24 06:12:29 EST 2020

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editing

approved

#22 by Alois P. Heinz at Fri Jan 24 06:12:26 EST 2020

CROSSREFS

Cf. A011782, A219727, A262809, A331315, A331485, A331636.

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approved

editing

#21 by Alois P. Heinz at Thu Jan 23 14:42:42 EST 2020

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editing

approved

#20 by Alois P. Heinz at Thu Jan 23 14:42:39 EST 2020

FORMULA

A(n,k) = Sum_{j=0..n*k} binomial(j+n-1,n)^k * (Sum_{i=j..n*k} (-1)^(i-j) * binomial(i,j)). - Andrew Howroyd, Jan 23 2020

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approved

editing

#19 by Alois P. Heinz at Thu Jan 23 14:42:11 EST 2020

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proposed

approved

#18 by Andrew Howroyd at Thu Jan 23 14:18:36 EST 2020

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editing

proposed