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A322126
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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.
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2
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%I #13 Nov 28 2018 07:11:02
%S 1,0,2,7188,134631576,7946203275000,1210527140790855600,
%T 411490045733601418421040,280031356887267221923677137280,
%U 351026687723982522494728236869341440,758933713536173718404757245269681913222400
%N 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.
%H Seiichi Manyama, <a href="/A322126/b322126.txt">Table of n, a(n) for n = 0..106</a>
%F a(n) = n! * A190833(n).
%F a(n) = Integral_{0..infinity} (x - 2 * x^2 + x^3 - 1/6 * x^4 + 1/120 * x^5)^n * exp(-x) dx.
%t 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 *)
%Y Row 5 of A322093.
%Y Cf. A190833, A322127, A322128.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 27 2018
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