A364524 Expansion of e.g.f. (1-x)^3/(1-3x+2x^2-x^3).

1, 0, 2, 18, 168, 1920, 26640, 433440, 8064000, 168739200, 3922732800, 100310918400, 2798327347200, 84569169484800, 2752393009766400, 95978067913728000, 3569951024640000000, 141085196791418880000, 5903699220162551808000, 260764276201191899136000, 12124067910801279713280000

Offset

0,3

Comments

a(n) is the number of ways to seat n persons on benches, linear order the benches, and select 2 persons from each bench.

A001804(n) is the number of ways if only 1 bench is used.

Links

Table of n, a(n) for n=0..20.

Example

a(6)=26640 since the number of ways to seat 6 persons on benches, linear order the benches, and select 2 persons from each bench is the following:
1) benches of type 1234,56: 1440 of these,  8640 ways;
2) benches of type 123,456:  720 of these,  6480 ways;
3) benches of type 12,34,56: 720 of these,   720 ways;
4) benches of type 123456:   720 of these, 10800 ways.

Mathematica

With[{max = 20}, Range[0, max]! * CoefficientList[Series[(1 - x)^3/(1 - 3*x + 2*x^2 - x^3), {x, 0, max}], x]] (* Amiram Eldar, Jul 28 2023 *)

Crossrefs

Cf. A001804, A002866.

Sequence in context: A052883 A052665 A259880 * A092473 A318218 A073558

Adjacent sequences: A364521 A364522 A364523 * A364525 A364526 A364527

Keyword

nonn

Author

Enrique Navarrete, Jul 27 2023

Status

approved