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A370530
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Number of permutations of [n] having exactly three adjacent 3-cycles.
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4
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0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 20, 116, 820, 6600, 59650, 598140, 6592740, 79232140, 1031214100, 14450182880, 216911207555, 3472641749080, 59063810100120, 1063582404217144, 20215010963623896, 404418346892678160, 8494912449554675844, 186928503912130116360
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OFFSET
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0,11
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LINKS
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FORMULA
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G.f.: (1/6) * Sum_{k>=3} k! * x^(k+6) / (1+x^3)^(k+1).
a(n) = (1/6) * Sum_{k=0..floor(n/3)-3} (-1)^k * (n-2*k-6)! / k!.
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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, 0, 0, 0], Vec(sum(k=3, N, k!*x^(k+6)/(1+x^3)^(k+1))/6))
(PARI) a(n, k=3, q=3) = 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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