A322126 Number of permutations of the multiset {1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,...,n,n,n,n,n} with no two consecutive terms equal.

1, 0, 2, 7188, 134631576, 7946203275000, 1210527140790855600, 411490045733601418421040, 280031356887267221923677137280, 351026687723982522494728236869341440, 758933713536173718404757245269681913222400

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..106

Formula

a(n) = n! * A190833(n).

a(n) = Integral_{0..infinity} (x - 2 * x^2 + x^3 - 1/6 * x^4 + 1/120 * x^5)^n * exp(-x) dx.

Mathematica

a[n_] := Integrate[(x - 2 * x^2 + x^3 - 1/6 * x^4 + 1/120 * x^5)^n * Exp[-x],  {x, 0, Infinity}]; Array[a, 10, 0] (* Stefano Spezia, Nov 27 2018 *)

Crossrefs

Row 5 of A322093.

Cf. A190833, A322127, A322128.

Sequence in context: A129058 A129057 A201508 * A272241 A171939 A104904

Adjacent sequences: A322123 A322124 A322125 * A322127 A322128 A322129

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2018

Status

approved