A321633 Number of permutations of the multiset {1,1,1,1,2,2,2,2,3,3,3,3,...,n,n,n,n} with no two consecutive terms equal.

1, 0, 2, 1092, 2265024, 11804626080, 131402141197200, 2778291737177034960, 102284730928300590754560, 6134232798447803932455457920, 568598490353320413296928514444800, 78076149156802562231395694989534464000, 15336188146163145199585928509793662920345600

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..129

Mathematics.StackExchange, Find the number of k 1's, k 2's, ... , k n's - total kn cards, Apr 08 2012.

Formula

a(n) = n! * A190830(n).

a(n) = Integral_{0..oo} (-x + 3/2 * x^2 - 1/2 * x^3 + 1/24 * x^4)^n * exp(-x) dx.

Example

a(2) = 2 because there are two permutations of {1,1,1,1,2,2,2,2} avoiding equal consecutive terms: 12121212 and 21212121.

Mathematica

a[n_] := Integrate[(-x + 3/2 * x^2 - 1/2 * x^3 + 1/24 * x^4)^n  * Exp[-x],  {x, 0, Infinity}]; Array[a, 10, 0] (* Stefano Spezia, Nov 27 2018 *)

Crossrefs

Row 4 of A322093.

Cf. A000142, A114938, A190830, A193638.

Sequence in context: A374334 A324590 A344669 * A244550 A359952 A039951

Adjacent sequences: A321630 A321631 A321632 * A321634 A321635 A321636

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2018

Status

approved