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.

User: J. Carlos Martínez Mori

J. Carlos Martínez Mori's wiki page.

J. Carlos Martínez Mori has authored 4 sequences.

A380082 Number of Boolean intervals of rank 2 in the weak order of the Coxeter group of type C_n, for n >= 2.

Original entry on oeis.org

0, 12, 288, 5760, 115200, 2419200, 54190080, 1300561920, 33443020800, 919683072000, 26977370112000, 841693947494400, 27852417898905600, 974834626461696000, 35993893900124160000, 1398619877261967360000, 57063690992288268288000, 2439472789920323469312000, 109058783549379166863360000
Offset: 2

Author

Keywords

Comments

Proof in Adenbaum et al., 2024 (full reference below).

Programs

  • PARI
    a(n) = n! * binomial(n-1, 2) * 2^(n-2); \\ Michel Marcus, Feb 19 2025

Formula

a(n) = n! * binomial(n - 1, 2) * 2^(n - 2).

Extensions

More terms from Michel Marcus, Feb 19 2025

A365627 Number of parking functions of length n with cars parking at most 4 spots away from their preferred spot.

Original entry on oeis.org

1, 1, 3, 16, 125, 1296, 15511, 212978, 3321091, 58196400, 1134161181, 24333706866, 569786870013, 14455456239756, 394940662364775, 11560567008386106, 360947377705705971, 11973823441677468648, 420576028975783973061, 15593290472977894193850
Offset: 0

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Crossrefs

Column k=4 of A365623.

A365623 T(n,k) is the number of parking functions of length n with cars parking at most k spots away from their preferred spot; square array T(n,k), n>=0, k>=0, read by downward antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 3, 6, 1, 1, 3, 13, 24, 1, 1, 3, 16, 75, 120, 1, 1, 3, 16, 109, 541, 720, 1, 1, 3, 16, 125, 918, 4683, 5040, 1, 1, 3, 16, 125, 1171, 9277, 47293, 40320, 1, 1, 3, 16, 125, 1296, 12965, 109438, 545835, 362880, 1, 1, 3, 16, 125, 1296, 15511, 166836, 1475691, 7087261, 3628800
Offset: 0

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Examples

			Square array T(n,k) begins:
    1,    1,    1,     1,     1,     1,     1, ...
    1,    1,    1,     1,     1,     1,     1, ...
    2,    3,    3,     3,     3,     3,     3, ...
    6,   13,   16,    16,    16,    16,    16, ...
   24,   75,  109,   125,   125,   125,   125, ...
  120,  541,  918,  1171,  1296,  1296,  1296, ...
  720, 4683, 9277, 12965, 15511, 16807, 16807, ...
  ...
		

Crossrefs

Columns k=0..1, 3..4 give: A000142, A000670, A365626, A365627.
Main diagonal gives A000272(n+1).
Cf. A264902.

Programs

  • Maple
    T:= proc(n, k) option remember; `if`(n=0, 1, add(min(i+1, k+1)*
           binomial(n-1, i)*T(i, k)*T(n-1-i, k), i=0..n-1))
        end:
    seq(seq(T(n, d-n), n=0..d), d=0..10);  # Alois P. Heinz, Sep 13 2023

Formula

T(n,k) = Sum_{i=0..n-1} binomial(n-1,i) * min(i+1,k+1) * T(i,k) * T(n-1-i,k) for n>0, T(0,k) = 1.

A365626 Number of parking functions of length n with cars parking at most 3 spots away from their preferred spot.

Original entry on oeis.org

1, 1, 3, 16, 125, 1171, 12965, 166836, 2455121, 40675881, 749029635, 15173252268, 335303622765, 8026962584007, 206940524177025, 5716136927184348, 168418082791822545, 5272347013042009125, 174760355153742270543, 6114528211048906800708, 225195326302815011830005
Offset: 0

Author

Keywords

Crossrefs

Column k=3 of A365623.