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.

Showing 1-4 of 4 results.

A123280 Number of permutations of n distinct letters (ABCD...) each of which appears 4 times and having two fixed points.

Original entry on oeis.org

0, 16, 4536, 8607744, 42506546320, 456702275019600, 9418598754396188616, 340409678708013417037696, 20126978659582117984569511584, 1844705433432528416880778883815440
Offset: 0

Views

Author

Zerinvary Lajos, Nov 07 2006

Keywords

Examples

			1
0, 0, "0", 0, 1
1, 0, "16", 0, 36, 0, 16, 0, 1
346, 1824, "4536", 7136, 7947, 6336, 3936, 1728, 684, 128, 48, 0, 1
748521, 3662976, "8607744", 12880512, 13731616, 11042688, 6928704, 3458432, 1395126, 453888, 122016, 25344, 4824, 512, 96, 0, 1
etc...

Crossrefs

Cf. A059060.

Programs

  • Maple
    p := (x, k)->k!^2*sum(x^j/((k-j)!^2*j!), j=0..k); R := (x, n, k)->p(x, k)^n; f := (t, n, k)->sum(coeff(R(x, n, k), x, j)*(t-1)^j*(n*k-j)!, j=0..n*k); for n from 0 to 5 do seq(coeff(f(t, n, 4), t, m)/4!^n, m=0..4*n); od;

A123292 Number of permutations of n distinct letters (ABCD...) each of which appears 4 times and having three fixed points.

Original entry on oeis.org

0, 0, 7136, 12880512, 61907282240, 654044867816320, 13334947538204224800, 477979874685352308242176, 28084174272553340151416556672, 2561385146102672068174078977972480
Offset: 0

Views

Author

Zerinvary Lajos, Nov 07 2006

Keywords

Examples

			1
0, 0, 0, "0", 1
1, 0, 16, "0", 36, 0, 16, 0, 1
346, 1824, 4536, "7136", 7947, 6336, 3936, 1728, 684, 128, 48, 0, 1
748521, 3662976, 8607744, "12880512", 13731616, 11042688, 6928704, 3458432, 1395126, 453888, 122016, 25344, 4824, 512, 96, 0, 1
3993445276, 18743463360, 42506546320, "61907282240", 64917874125, 52087325696, 33176621920, 17181584640, 7352761180, 2628808000, 790912656, 201062080, 43284010, 7873920, 1216000, 154496, 17640, 1280, 160, 0, 1
etc..

Crossrefs

Cf. A059060.

Programs

  • Maple
    p := (x, k)->k!^2*sum(x^j/((k-j)!^2*j!), j=0..k); R := (x, n, k)->p(x, k)^n; f := (t, n, k)->sum(coeff(R(x, n, k), x, j)*(t-1)^j*(n*k-j)!, j=0..n*k); for n from 0 to 5 do seq(coeff(f(t, n, 4), t, m)/4!^n, m=0..4*n); od;

A123293 Number of permutations of n distinct letters (ABCD...) each of which appears 4 times and having n-3 fixed points.

Original entry on oeis.org

0, 0, 128, 512, 1280, 2560, 4480, 7168, 10752, 15360, 21120, 28160
Offset: 0

Views

Author

Zerinvary Lajos, Nov 07 2006

Keywords

Examples

			1
0, "0", 0, 0, 1
1, 0, 16, 0, 36, "0", 16, 0, 1
346, 1824, 4536, 7136, 7947, 6336, 3936, 1728, 684, "128", 48, 0, 1
748521, 3662976, 8607744, 12880512, 13731616, 11042688, 6928704, 3458432, 1395126, 453888, 122016, 25344, 4824, "512", 96, 0, 1
3993445276, 18743463360, 42506546320, 61907282240, 64917874125, 52087325696, 33176621920, 17181584640, 7352761180, 2628808000, 790912656, 201062080, 43284010, 7873920, 1216000, 154496, 17640, "1280", 160, 0, 1
etc..

Crossrefs

Cf. A059060.

Programs

  • Maple
    p := (x, k)->k!^2*sum(x^j/((k-j)!^2*j!), j=0..k); R := (x, n, k)->p(x, k)^n; f := (t, n, k)->sum(coeff(R(x, n, k), x, j)*(t-1)^j*(n*k-j)!, j=0..n*k); for n from 0 to 5 do seq(coeff(f(t, n, 4), t, m)/4!^n, m=0..4*n); od;

A124073 Number of permutations of n distinct letters (ABCD...) each of which appears 4 times with one fixed point.

Original entry on oeis.org

0, 0, 1824, 3662976, 18743463360, 206032439164800, 4316868116405748960, 157846181105000772889344, 9416135162778291726755147136, 869099332136838873667455070091520, 118924204222864960529120670496333629600, 23292190275693669075772234927951426886017920
Offset: 1

Views

Author

Zerinvary Lajos, Nov 05 2006

Keywords

Examples

			A059060 as a triangle:
1
0, "0", 0, 0, 1
1, "0", 16, 0, 36, 0, 16, 0, 1
346, "1824", 4536, 7136, 7947, 6336, 3936, 1728, 684, 128, 48, 0, 1
748521, "3662976", 8607744, 12880512, 13731616, 11042688, 6928704, 3458432, 1395126, 453888, 122016, 25344, 4824, 512, 96, 0, 1
3993445276, "18743463360", 42506546320, 61907282240, 64917874125, 52087325696, 33176621920, 17181584640, 7352761180, 2628808000, 790912656, 201062080, 43284010, 7873920, 1216000, 154496, 17640, 1280, 160, 0, 1

Crossrefs

Cf. A059060.

Programs

  • Maple
    p := (x, k)->k!^2*sum(x^j/((k-j)!^2*j!), j=0..k);
R := (x, n, k)->p(x, k)^n;
f := (t, n, k)->sum(coeff(R(x, n, k), x, j)*(t-1)^j*(n*k-j)!, j=0..n*k);
# copied from A059060
seq(coeff(f(t, n, 4), t, 1)/4!^n, n=1..12);

Formula

a(n) = A059060(n, 1). - Joerg Arndt, Nov 08 2020

Extensions

Offset corrected by Joerg Arndt, Nov 08 2020
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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