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A059045
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Square array T(n,k) read by antidiagonals where T(0,k) = 0 and T(n,k) = 1 + 2k + 3k^2 + ... + n*k^(n-1).
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4
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0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 6, 5, 1, 0, 1, 10, 17, 7, 1, 0, 1, 15, 49, 34, 9, 1, 0, 1, 21, 129, 142, 57, 11, 1, 0, 1, 28, 321, 547, 313, 86, 13, 1, 0, 1, 36, 769, 2005, 1593, 586, 121, 15, 1, 0, 1, 45, 1793, 7108, 7737, 3711, 985, 162, 17, 1, 0, 1, 55, 4097, 24604, 36409
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OFFSET
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0,8
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LINKS
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FORMULA
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T(n,k) = n*k^(n-1)+T(n-1, k) = (n*k^(n+1)-(n+1)*k^n+1)/(k-1)^2.
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EXAMPLE
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0, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 3, 5, 7, 9, 11, 13, 15, 17, ...
1, 6, 17, 34, 57, 86, 121, 162, 209, ...
1, 10, 49, 142, 313, 586, 985, 1534, 2257, ...
1, 15, 129, 547, 1593, 3711, 7465, 13539, 22737, ...
1, 21, 321, 2005, 7737, 22461, 54121, 114381, 219345, ...
1, 28, 769, 7108, 36409, 131836, 380713, 937924, 2054353, ...
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MAPLE
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if k = 1 then
n*(n+1) /2 ;
else
(1+n*k^(n+1)-k^n*(n+1))/(k-1)^2 ;
end if;
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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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