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A370392
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Number of permutations of [n] whose longest block is of length 3. A block of a permutation is a maximal sequence of consecutive integers which appear in consecutive positions.
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2
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0, 0, 0, 1, 2, 11, 63, 415, 3121, 26402, 248429, 2575936, 29198926, 359351878, 4773277246, 68078349863, 1037820312090, 16842621113247, 289946286959875, 5277826030457339, 101291053229162471, 2044252472193005928, 43283094591188747415, 959369370636209414390
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OFFSET
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0,5
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} k! * x^k * ( ((1-x^3)/(1-x^4))^k - ((1-x^2)/(1-x^3))^k ).
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PROG
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(PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=0, N, k!*x^k*(((1-x^3)/(1-x^4))^k-((1-x^2)/(1-x^3))^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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