The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A199012 The total number of edges in all unlabeled directed graphs (no self loops allowed) on n nodes. 0
 0, 3, 48, 1308, 96080, 23114160, 18522702240, 50214057399744, 469006445678383872, 15356719437883766115840, 1788760016178073736115859200, 750205198434476437912637004278784, 1144188684031608529784893493874665232384, 6398724751986384956446081096594171272300830720 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..14. FORMULA a(n) = A000273(n) * n(n-1)/2. a(n) = Sum_{k=1..n*(n-1)} k*A052283(n,k). - Andrew Howroyd, Nov 05 2017 MAPLE b:= proc(n, i, l) `if`(n=0 or i=1, 1/n!*2^((p-> add(p[j]-1+add( igcd(p[k], p[j]), k=1..j-1)*2, j=1..nops(p)))([l[], 1\$n])), add(b(n-i*j, i-1, [l[], i\$j])/j!/i^j, j=0..n/i)) end: a:= n-> b(n\$2, [])*n*(n-1)/2: seq(a(n), n=1..16); # Alois P. Heinz, Sep 04 2019 MATHEMATICA Table[D[GraphPolynomial[n, x, Directed], x]/.x->1, {n, 1, 15}] (* Second program: *) permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m]; edges[v_, t_] := Product[g = GCD[v[[i]], v[[j]]]; t[v[[i]]*v[[j]]/g]^(2*g), {i, 2, Length[v]}, {j, 1, i - 1}] * Product[ t[v[[i]]]^(v[[i]] - 1), {i, 1, Length[v]}] a[n_] := (s = 0; Do[s += permcount[p]*(D[edges[p, 1 + x^# &], x] /. x -> 1), {p, IntegerPartitions[n]}]; s/n!); Array[a, 15] (* Jean-François Alcover, Jul 08 2018, after Andrew Howroyd *) PROG (PARI) permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m} edges(v, t) = {prod(i=2, #v, prod(j=1, i-1, my(g=gcd(v[i], v[j])); t(v[i]*v[j]/g)^(2*g))) * prod(i=1, #v, t(v[i])^(v[i]-1))} a(n) = {my(s=0); forpart(p=n, s+=permcount(p)*subst(deriv(edges(p, i->1+x^i)), x, 1)); s/n!} \\ Andrew Howroyd, Nov 05 2017 CROSSREFS Cf. A000273, A052283, A086314. Sequence in context: A320668 A319732 A351424 * A304208 A300871 A341498 Adjacent sequences: A199009 A199010 A199011 * A199013 A199014 A199015 KEYWORD nonn AUTHOR Geoffrey Critzer, Nov 01 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 25 03:08 EDT 2024. Contains 372782 sequences. (Running on oeis4.)