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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.
5
1, 0, 2, 1092, 2265024, 11804626080, 131402141197200, 2778291737177034960, 102284730928300590754560, 6134232798447803932455457920, 568598490353320413296928514444800, 78076149156802562231395694989534464000, 15336188146163145199585928509793662920345600
OFFSET
0,3
LINKS
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.
Sequence in context: A374334 A324590 A344669 * A244550 A359952 A039951
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 15 2018
STATUS
approved