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A300851
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Number of 6-cycles in the n-transposition graph.
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3
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0, 0, 6, 2880, 83400, 1742400, 32810400, 600606720, 11049696000, 207712512000, 4024212192000, 80721349632000, 1680305519692800, 36334168206336000, 816328800967680000, 19051455560417280000, 461604030434426880000, 11603252352344260608000
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = n!*(binomial(n,3) + 116*binomial(n,4) + 105*binomial(n,5) + 30*binomial(n,6)). - Andrew Howroyd, Mar 13 2018
a(n) = n!*binomial(n, 3)*(n^3 + 9*n^2 + 16*n - 152)/4.
E.g.f.: x^3*(1+113*x-124*x^2+40*x^3)/(1-x)^7. - Robert Israel, Mar 14 2018
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MAPLE
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seq(n!*binomial(n, 3)*(n^3 + 9*n^2 + 16*n - 152)/4, n=1..30); # Robert Israel, Mar 14 2018
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MATHEMATICA
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Table[n! Binomial[n, 3] (n^3 + 9 n^2 + 16 n - 152)/4, {n, 20}]
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PROG
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(PARI) a(n) = n!*(binomial(n, 3) + 116*binomial(n, 4) + 105*binomial(n, 5) + 30*binomial(n, 6)); \\ Andrew Howroyd, Mar 13 2018
(PARI) x='x+O('x^99); concat([0, 0], Vec(serlaplace(x^3*(1+113*x-124*x^2+40*x^3)/(1-x)^7))) \\ Altug Alkan, Mar 14 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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