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A125092
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Triangle read by rows: T(n,k) = (k+1)^2*binomial(n,k) (0 <= k <= n).
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2
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1, 1, 4, 1, 8, 9, 1, 12, 27, 16, 1, 16, 54, 64, 25, 1, 20, 90, 160, 125, 36, 1, 24, 135, 320, 375, 216, 49, 1, 28, 189, 560, 875, 756, 343, 64, 1, 32, 252, 896, 1750, 2016, 1372, 512, 81, 1, 36, 324, 1344, 3150, 4536, 4116, 2304, 729, 100, 1, 40, 405, 1920, 5250, 9072
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OFFSET
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0,3
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COMMENTS
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Binomial transform of the infinite diagonal matrix (1,4,9,16,...).
Sum of entries in row n = (n+1)*(n+4)*2^(n-2) = A001793(n+1).
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LINKS
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EXAMPLE
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First few rows of the triangle:
1;
1, 4;
1, 8, 9;
1, 12, 27, 16;
1, 16, 54, 64, 25;
1, 20, 90, 160, 125, 36;
...
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MAPLE
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T:=(n, k)->(k+1)^2*binomial(n, k): for n from 0 to 11 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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MATHEMATICA
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Table[(k+1)^2 Binomial[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Feb 20 2023 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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