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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 15 2018
STATUS
approved