A365293 - OEIS

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

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OFFSET

0,3

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.

LINKS

Table of n, a(n) for n=0..19.

FORMULA

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

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

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A259868 A036691 A349514 * A293021 A002866 A182798

Adjacent sequences: A365290 A365291 A365292 * A365294 A365295 A365296

KEYWORD

nonn

AUTHOR

Enrique Navarrete, Aug 31 2023

STATUS

approved