A300851 Number of 6-cycles in the n-transposition graph.

0, 0, 6, 2880, 83400, 1742400, 32810400, 600606720, 11049696000, 207712512000, 4024212192000, 80721349632000, 1680305519692800, 36334168206336000, 816328800967680000, 19051455560417280000, 461604030434426880000, 11603252352344260608000

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..444

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

Adjacent sequences: A300848 A300849 A300850 * A300852 A300853 A300854

Keyword

nonn

Author

Eric W. Weisstein, Mar 13 2018

Extensions

Terms a(9) and beyond from Andrew Howroyd, Mar 13 2018

Status

approved