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A265080
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Array read by antidiagonals, arising from study of remixing keys in public-key cryptography.
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6
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0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 6, 3, 0, 0, 4, 12, 18, 4, 0, 0, 5, 20, 51, 44, 5, 0, 0, 6, 30, 108, 192, 110, 6, 0, 0, 7, 42, 195, 544, 675, 252, 7, 0, 0, 8, 56, 318, 1220, 2540, 2358, 588, 8, 0, 0, 9, 72, 483, 2364, 7145, 11544, 8043, 1304, 9, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,8
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COMMENTS
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See Brown (2015) for precise definition.
If you randomly throw n balls into k boxes then T(n,k)/k^n is the expected number of balls in the fullest box. - Henry Bottomley, Mar 20 2021
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LINKS
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EXAMPLE
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Array begins:
0, 0, 0, 0, 0, 0, ...
0, 1, 2, 3, 4, 5, ...
0, 2, 6, 12, 20, 30, ...
0, 3, 18, 51, 108, 195, ...
0, 4, 44, 192, 544, 1220, ...
0, 5, 110, 675, 2540, 7145, ...
...
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PROG
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(PARI) Q(p)={my(S=Set(p)); prod(i=1, #S, (#select(t->t==S[i], p))!)}
T(n, k)={my(s=0); forpart(p=n, s+=p[#p]*n!*(#p)!*binomial(k, #p)/(prod(i=1, #p, p[i]!) * Q(Vec(p)))); s} \\ Andrew Howroyd, Mar 20 2021
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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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