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A099240
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Main diagonal of A099239.
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2
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1, 2, 8, 41, 250, 1757, 13917, 122166, 1173662, 12222605, 136927351, 1639768418, 20880556880, 281460326864, 4000651782511, 59761935358025, 935445106491702, 15303039199768237, 261030618751031385, 4632889302298054713
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{j=0..n} binomial(n^2 - (n-1)*(j-1), j).
a(n) = Sum_{j=0..n} binomial(n + (n-1)*(j+1), n*(j+1) - 1) with a(0) = 1.
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MATHEMATICA
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Table[Sum[Binomial[n^2 -(n-1)*(j-1), j], {j, 0, n}], {n, 0, 30}] (* G. C. Greubel, Mar 09 2021 *)
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PROG
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(Sage) [sum(binomial(n^2 -(n-1)*(j-1), j) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Mar 09 2021
(Magma) [1] cat [(&+[Binomial(n+(n-1)*(j+1), n*(j+1)-1): j in [0..n]]): n in [1..30]]; // G. C. Greubel, Mar 09 2021
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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