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A306444
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A(n,k) = binomial((2*k+1)*n+2, k*n+1)/((2*k+1)*n+2), square array A(n,k) read by antidiagonals, for n >= 0, k >= 0.
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4
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1, 1, 1, 1, 2, 1, 1, 5, 7, 1, 1, 14, 66, 30, 1, 1, 42, 715, 1144, 143, 1, 1, 132, 8398, 49742, 22610, 728, 1, 1, 429, 104006, 2340135, 3991995, 482885, 3876, 1, 1, 1430, 1337220, 115997970, 757398510, 347993910, 10855425, 21318, 1
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OFFSET
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0,5
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LINKS
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, ...
1, 2, 5, 14, 42, ...
1, 7, 66, 715, 8398, ...
1, 30, 1144, 49742, 2340135, ...
1, 143, 22610, 3991995, 757398510, ...
1, 728, 482885, 347993910, 267058714626, ...
1, 3876, 10855425, 32018897274, 99543581789652, ...
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MATHEMATICA
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A[n_, k_]:= Binomial[(2*k+1)*n+2, k*n+1]/((2*k+1)*n+2); Table[A[k, n-k], {n, 0, 12}, {k, 0, n}] (* G. C. Greubel, Feb 16 2019 *)
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PROG
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(PARI) {A(n, k) = binomial((2*k+1)*n+2, k*n+1)/((2*k+1)*n+2)};
for(n=0, 12, for(k=0, n, print1(A(k, n-k), ", "))) \\ G. C. Greubel, Feb 16 2019
(Magma) [[Binomial((2*(n-k)+1)*k+2, k*(n-k)+1)/((2*(n-k)+1)*k+2): k in [0..n]]: n in [0..12]]; // G. C. Greubel, Feb 16 2019
(Sage) [[binomial((2*(n-k)+1)*k+2, k*(n-k)+1)/((2*(n-k)+1)*k+2) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Feb 16 2019
(GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial((2*(n-k)+1)*k+2, k*(n-k)+1)/((2*(n-k)+1)*k+2) ))); # G. C. Greubel, Feb 16 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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