OFFSET
1,5
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..400
P. J. Cameron, Counting two-graphs related to trees, Elec. J. Combin., Vol. 2, #R4.
FORMULA
a(n) = A005512(n+1) / (n+1) for n >= 2. - Sean A. Irvine, Feb 03 2018
E.g.f.: 1/(2*x) + (x-1)/2 - ((1+x)/(2*x))*(1 + LambertW(-x/(1+x)))^2. - G. C. Greubel, Mar 08 2020
MAPLE
seq( `if`(n=1, 1, (n-1)!*add((-1)^k*binomial(n+1, k)*(n-k+1)^(n-k-1)/( (n+1)*(n-k-1)!), k = 0..n-1)), n=1..20); # G. C. Greubel, Mar 08 2020
MATHEMATICA
Table[If[n==1, 1, (n-1)!*Sum[(-1)^k*Binomial[n+1, k]*(n-k+1)^(n-k-1)/((n+1)*(n - k-1)!), {k, 0, n-1}]], {n, 20}] (* G. C. Greubel, Mar 08 2020 *)
PROG
(PARI) a(n) = if(n==1, 1, (n-1)!*sum(k=0, n-1, (-1)^k*binomial(n+1, k)*(n-k+1 )^(n-k-1)/( (n+1)*(n-k-1)!))); \\ G. C. Greubel, Mar 08 2020
(Magma) [1] cat [Factorial(n-1)*(&+[(-1)^k*Binomial(n+1, k)*(n-k+1)^(n-k-1)/((n+1)*Factorial(n-k-1)): k in [0..n-1]]): n in [2..20]] // G. C. Greubel, Mar 08 2020
(Sage) [1]+[factorial(n-1)*sum((-1)^k*binomial(n+1, k)*(n-k+1)^(n-k-1)/( (n+1)*factorial(n-k-1)) for k in (0..n-1)) for n in (2..20)] # G. C. Greubel, Mar 08 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved