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A300851 Number of 6-cycles in the n-transposition graph. 3
0, 0, 6, 2880, 83400, 1742400, 32810400, 600606720, 11049696000, 207712512000, 4024212192000, 80721349632000, 1680305519692800, 36334168206336000, 816328800967680000, 19051455560417280000, 461604030434426880000, 11603252352344260608000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Transposition Graph
FORMULA
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
MAPLE
seq(n!*binomial(n, 3)*(n^3 + 9*n^2 + 16*n - 152)/4, n=1..30); # Robert Israel, Mar 14 2018
MATHEMATICA
Table[n! Binomial[n, 3] (n^3 + 9 n^2 + 16 n - 152)/4, {n, 20}]
PROG
(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
CROSSREFS
Cf. A300843 (4-cycles).
Sequence in context: A198667 A225066 A001326 * A089501 A290149 A187083
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Mar 13 2018
EXTENSIONS
Terms a(9) and beyond from Andrew Howroyd, Mar 13 2018
STATUS
approved

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)