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A300843 Number of 4-cycles in the n-transposition graph. 2
0, 0, 9, 162, 2250, 29700, 396900, 5503680, 80015040, 1224720000, 19758816000, 335899872000, 6010631827200, 113048449113600, 2231219390400000, 46134751703040000, 997703235809280000, 22529953070456832000, 530433460332711936000, 13000820106193920000000 (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) = 3*n!*(2*binomial(n,3) + binomial(n,4))/4. - Andrew Howroyd, Mar 13 2018
E.g.f.: 3*x^2*(2-x)/(4*(1-x)^5). - Robert Israel, Mar 14 2018
MATHEMATICA
Table[3 n! (2 Binomial[n, 3] + Binomial[n, 4])/4, {n, 25}] (* Vincenzo Librandi, Mar 14 2018 *)
Table[3 (n + 5) Binomial[n, 3] n!/16, {n, 20}] (* Eric W. Weisstein, Mar 14 2018 *)
PROG
(PARI) a(n)={3*n!*(2*binomial(n, 3)+binomial(n, 4))/4} \\ Andrew Howroyd, Mar 13 2018
(Magma) [3*Factorial(n)*(2*Binomial(n, 3)+Binomial(n, 4))/4: n in [1..20]]; // Vincenzo Librandi, Mar 14 2018
CROSSREFS
Cf. A300851 (6-cycles), A296528.
Sequence in context: A209962 A084874 A158749 * A133681 A157553 A202438
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 June 16 19:52 EDT 2024. Contains 373432 sequences. (Running on oeis4.)