A365293 a(n) = n!*tetranacci(n+3).

1, 1, 4, 24, 192, 1800, 20880, 282240, 4354560, 75479040, 1455148800, 30855686400, 713712384000, 17884003737600, 482619020083200, 13954193180928000, 430360865206272000, 14102295149150208000, 489295008086556672000, 17919783031425859584000

Offset: 0

Author

Enrique Navarrete, Aug 31 2023

Keywords

• nonn

Comments

a(n) is the number of ways to partition [n] into blocks of size at most 4, order the blocks, and order the elements within each block.

Examples

			a(5) = 1800 since the number of ways to partition [5] into blocks of size at most 4, order the blocks, and order the elements within each block are the following:
1) 1234,5: 10 such ordered blocks; 240 ways;
2) 123,4,5: 60 such ordered blocks; 360 ways;
3) 123,45: 20 such ordered blocks; 240 ways;
4) 12,34,5: 90 such ordered blocks; 360 ways;
5) 12,3,4,5: 240 such ordered blocks; 480 ways;
6) 1,2,3,4,5: 120 such ordered blocks; 120 ways.
		

Crossrefs

Cf. A000078, A000142, A002866, A005442, A276924, A364324.

Programs

Mathematica

Table[n! SeriesCoefficient[1/(1-x-x^2-x^3-x^4),{x,0,n}],{n,0,19}] (* Stefano Spezia, Aug 31 2023 *)

Formula

E.g.f.: 1/(1-x-x^2-x^3-x^4).

a(n) = A000142(n) * A000078(n+3).