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.

A352367 Row sums of A352366.

Original entry on oeis.org

1, 1, 2, 6, 23, 105, 552, 3276, 21632, 157058, 1241542, 10599358, 97078720, 948631866, 9844060930, 108045790170, 1249891268947, 15192207346713, 193489732812832, 2575819322454708, 35763019798305487, 516830453606687539, 7760160395056532042, 120860540786892879030
Offset: 0

Views

Author

Peter Luschny, Mar 15 2022

Keywords

Comments

a(n) is the number of chordal graphs with fixed symmetric perfect elimination ordering; i.e., graphs on V = [n] such that 1,...,n and n,...,1 are perfect elimination orderings. - Robert Lauff, Jan 25 2023
a(n) is the number of labeled unit-interval-graphs. This is because connected labeled unit-interval-graphs are a Catalan family. Given a partition of [n], we draw a connected unit-interval-graph for each of the partition classes. This weights the partitions with a Catalan number. The connection to my previous comment can be shown by induction. - Robert Lauff, Feb 01 2023

Links

Crossrefs

Cf. A000108, A352366.

A352368 Alternating row sums of A352366.

Original entry on oeis.org

1, -1, 0, 0, 1, 5, 18, 42, -58, -1664, -14502, -90574, -382846, 114556, 26040038, 376126350, 3773076517, 28273327725, 111536583430, -1134493414034, -36043045939893, -581994648802655, -7078387642902232, -63895288842031656, -248139475138765108, 6030827802781277326
Offset: 0

Views

Author

Peter Luschny, Mar 15 2022

Keywords

Crossrefs

Cf. A352366.

A352363 Triangle read by rows. The incomplete Bell transform of the swinging factorials A056040.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 0, 6, 11, 6, 1, 0, 6, 50, 35, 10, 1, 0, 30, 166, 225, 85, 15, 1, 0, 20, 756, 1246, 735, 175, 21, 1, 0, 140, 2932, 7588, 5761, 1960, 322, 28, 1, 0, 70, 11556, 45296, 46116, 20181, 4536, 546, 36, 1
Offset: 0

Views

Author

Peter Luschny, Mar 15 2022

Keywords

Examples

			Triangle starts:
[0] 1;
[1] 0,   1;
[2] 0,   1,     1;
[3] 0,   2,     3,     1;
[4] 0,   6,    11,     6,     1;
[5] 0,   6,    50,    35,    10,     1;
[6] 0,  30,   166,   225,    85,    15,    1;
[7] 0,  20,   756,  1246,   735,   175,   21,   1;
[8] 0, 140,  2932,  7588,  5761,  1960,  322,  28, 1;
[9] 0,  70, 11556, 45296, 46116, 20181, 4536, 546, 36, 1;

Crossrefs

Cf. A056040, A352364 (row sums), A352365 (alternating row sums).
Cf. A352366, A352369.

Programs

  • Maple
    SwingNumber := n -> n! / iquo(n, 2)!^2:
for n from 0 to 9 do
seq(IncompleteBellB(n, k, seq(SwingNumber(j), j = 0..n)), k = 0..n) od;

Formula

Given a sequence s let s|n denote the initial segment s(0), s(1), ..., s(n).
(T(s))(n, k) = IncompleteBellPolynomial(n, k, s|n), where s(n) = n!/floor(n/2)!^2.

A352369 Triangle read by rows. The incomplete Bell transform of the central binomial numbers.

Original entry on oeis.org

1, 0, 1, 0, 2, 1, 0, 6, 6, 1, 0, 20, 36, 12, 1, 0, 70, 220, 120, 20, 1, 0, 252, 1380, 1140, 300, 30, 1, 0, 924, 8904, 10710, 4060, 630, 42, 1, 0, 3432, 59024, 101136, 52640, 11480, 1176, 56, 1, 0, 12870, 400824, 966672, 671328, 195300, 27720, 2016, 72, 1
Offset: 0

Views

Author

Peter Luschny, Mar 15 2022

Keywords

Examples

			Triangle starts:
[0] 1;
[1] 0,     1;
[2] 0,     2,      1;
[3] 0,     6,      6,      1;
[4] 0,    20,     36,     12,      1;
[5] 0,    70,    220,    120,     20,      1;
[6] 0,   252,   1380,   1140,    300,     30,     1;
[7] 0,   924,   8904,  10710,   4060,    630,    42,    1;
[8] 0,  3432,  59024, 101136,  52640,  11480,  1176,   56,  1;
[9] 0, 12870, 400824, 966672, 671328, 195300, 27720, 2016, 72, 1;

Crossrefs

Cf. A000984, A352370 (row sums), A352371 (alternating row sums).
Cf. A352363, A352366.

Programs

  • Maple
    CentralBinomial := n -> binomial(2*n, n):
for n from 0 to 9 do
seq(IncompleteBellB(n, k, seq(CentralBinomial(j), j = 0..n)), k = 0..n) od;

Formula

Given a sequence s let s|n denote the initial segment s(0), s(1), ..., s(n).
(T(s))(n, k) = IncompleteBellPolynomial(n, k, s|n) where s(n) = binomial(2*n, n).
Showing 1-4 of 4 results.

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

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