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A370529
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Number of permutations of [n] having exactly three adjacent 2-cycles.
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4
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0, 0, 0, 0, 0, 0, 1, 4, 16, 100, 730, 5940, 54160, 547540, 6077155, 73473400, 961231264, 13530711096, 203921897844, 3276281076600, 55900700199840, 1009488884673720, 19236189509000805, 385733279064689820, 8119635049867486640, 179017704376149395900
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OFFSET
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0,8
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LINKS
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FORMULA
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G.f.: (1/6) * Sum_{k>=3} k! * x^(k+3) / (1+x^2)^(k+1).
a(n) = (1/6) * Sum_{k=0..floor(n/2)-3} (-1)^k * (n-k-3)! / k!.
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MAPLE
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a:= proc(n) option remember; `if`(n<7, [0$6, 1][n+1], ((n-5)*(n-6)*(n-3)*a(n-1)
-6*(n-4)*a(n-2)+(n-2)*(n-3)*((n-5)*a(n-3)+a(n-4)))/((n-5)*(n-6)))
end:
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PROG
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(PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0, 0, 0, 0], Vec(sum(k=3, N, k!*x^(k+3)/(1+x^2)^(k+1))/6))
(PARI) a(n, k=3, q=2) = sum(j=0, n\q-k, (-1)^j*(n-(q-1)*(j+k))!/j!)/k!;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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