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A092393
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Triangle read by rows: T(n,k) = (n+k)*binomial(n,k) (for k=0..n-1).
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1
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1, 2, 6, 3, 12, 15, 4, 20, 36, 28, 5, 30, 70, 80, 45, 6, 42, 120, 180, 150, 66, 7, 56, 189, 350, 385, 252, 91, 8, 72, 280, 616, 840, 728, 392, 120, 9, 90, 396, 1008, 1638, 1764, 1260, 576, 153, 10, 110, 540, 1560, 2940, 3780, 3360, 2040, 810, 190, 11, 132, 715
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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FORMULA
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First column = positive integers;
main diagonal (i.e., T(n,n) = (n+n)*binomial(n,n) = 2n, which is not included in this sequence) = even integers;
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EXAMPLE
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Triangle starts:
1;
2, 6;
3, 12, 15;
4, 20, 36, 28;
5, 30, 70, 80, 45;
6, 42, 120, 180, 150, 66;
...
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MAPLE
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(n+k)*binomial(n, k) ;
end proc:
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MATHEMATICA
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A092393row[n_]:=Table[(n+k)Binomial[n, k], {k, 0, n-1}]; Array[A092393row, 10] (* Paolo Xausa, Nov 02 2023 *)
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PROG
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(PARI) T(n, k)=binomial(n, k)*(n+k)
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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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