OFFSET
1,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
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
From Amiram Eldar, Oct 25 2025: (Start)
Sum_{n>=3} 1/a(n) = (176*e + 104*(gamma - Ei(1)))/105 - 34544/11025, where e = A001113, Ei(1) = A091725, and gamma = A001620.
Sum_{n>=3} (-1)^(n+1)/a(n) = 1016*(gamma - Ei(-1))/105 - 320/(21*e) - 22016/11025, where Ei(-1) = -A099285. (End)
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 13 2018
EXTENSIONS
Terms a(9) and beyond from Andrew Howroyd, Mar 13 2018
STATUS
approved