cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A323805 Number of permutations p of [n] such that max_{j=1..n} |p(j)-j| = 9.

Original entry on oeis.org

0, 685440, 11123280, 124658640, 1166388360, 9804325176, 77191636698, 585120530242, 4352418785279, 32202026068621, 240183024181127, 1821246237562657, 13946936520272756, 107314021044232924, 826507136709547152, 6354476077005199296, 48686592289143593088
Offset: 9

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Author

Alois P. Heinz, Jan 28 2019

Keywords

Crossrefs

Column k=9 of A130152.

Formula

a(n) = A154658(n) - A154657(n).

A323806 Number of permutations p of [n] such that max_{j=1..n} |p(j)-j| = 10.

Original entry on oeis.org

0, 6894720, 125516160, 1586345040, 16759964880, 158705713320, 1400777573016, 11828309150490, 97341704612482, 791331470025483, 6418149695049249, 52479230675397803, 435575075749110957, 3649912769065068556, 30745771540084745428, 259496462836442105424
Offset: 10

Views

Author

Alois P. Heinz, Jan 28 2019

Keywords

Crossrefs

Column k=10 of A130152.

Formula

a(n) = A154659(n) - A154658(n).

A323807 Number of permutations p of [n] such that max_{j=1..n} |p(j)-j| = floor(n/2).

Original entry on oeis.org

1, 1, 2, 9, 23, 157, 503, 4833, 18827, 234061, 1076807, 16447329, 87358763, 1583571277, 9541763303, 200258110593, 1350025656107, 32202026068621, 240183024181127, 6418149695049249, 52479230675397803, 1553052337531253197, 13814973114258788903, 448537638127408597953, 4312466658317635366187
Offset: 1

Views

Author

Alois P. Heinz, Jan 28 2019

Keywords

Examples

			a(4) = 9: 1342, 1423, 1432, 2314, 2413, 3124, 3142, 3214, 3412.
a(5) = 23: 12453, 12534, 12543, 13425, 13524, 14235, 14253, 14325, 14523, 21453, 21534, 21543, 23145, 23154, 24135, 24153, 31245, 31254, 31425, 31524, 32145, 32154, 34125.
		

Crossrefs

Cf. A130152.

Formula

a(n) = A130152(n,floor(n/2)).

A364817 Triangle read by rows: T(n,k) = number of permutations p of [n] such that max(|p(p(i)) - i|)=k (n>=1, 0<=k<=n-1).

Original entry on oeis.org

1, 2, 0, 4, 0, 2, 10, 2, 6, 6, 26, 6, 22, 36, 30, 76, 24, 92, 144, 216, 168, 232, 80, 334, 640, 1150, 1524, 1080, 764, 312, 1328, 2984, 5516, 9712, 11784, 7920, 2620, 1152, 5234, 13296, 27668, 55750, 90240, 101400, 65520, 9496, 4616, 21780, 62124, 144564, 306272, 601756, 909312, 964080, 604800
Offset: 1

Views

Author

Seiichi Manyama, Oct 21 2023

Keywords

Examples

			Triangle starts:
     1;
     2,    0;
     4,    0,    2;
    10,    2,    6,     6;
    26,    6,   22,    36,    30;
    76,   24,   92,   144,   216,   168;
   232,   80,  334,   640,  1150,  1524,  1080;
   764,  312, 1328,  2984,  5516,  9712, 11784,   7920;
  2620, 1152, 5234, 13296, 27668, 55750, 90240, 101400, 65520;
		

Crossrefs

Columns k=0..1 give: A000085, A364819.
Row sums give A000142.

Formula

T(n,n-1) = (2*n-5)*(n-2)! for n>3.
Previous Showing 11-14 of 14 results.