A265080 Array read by antidiagonals, arising from study of remixing keys in public-key cryptography.

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

Offset

0,8

Comments

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

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325

Daniel R. L. Brown, Bounds on surmising remixed keys, IACR, Report 2015/375, 2015-2016. See Table 1.

Example

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, ...
  ...

Prog

(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

Crossrefs

Rows n=1..5 are A001477, A002378, A064043, A265081, A265082.

Columns k=1..5 are A001477, A230137, A265083, A265084, A265085.

Main diagonal is A208250.

Sequence in context: A343046 A271917 A185651 * A228275 A228250 A341317

Adjacent sequences: A265077 A265078 A265079 * A265081 A265082 A265083

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jan 01 2016

Extensions

More terms from Henry Bottomley, Mar 20 2021

Status

approved