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A053516 Number of directed 4-multigraphs with loops on n nodes. 5
5, 325, 327125, 6360324375, 2483590604688125, 20211024423069510171875, 3524517841661451239027963515625, 13444967478414031326768049544880110156250, 1139744010069698074379093986222808985702884783203125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..30

MATHEMATICA

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_] := Sum[2*GCD[v[[i]], v[[j]]], {i, 2, Length[v]}, {j, 1, i - 1}] + Total[v];

a[n_] := (s=0; Do[s += permcount[p]*5^edges[p], {p, IntegerPartitions[n]}]; s/n!);

Array[a, 15] (* Jean-Fran├žois 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) = {sum(i=2, #v, sum(j=1, i-1, 2*gcd(v[i], v[j]))) + sum(i=1, #v, v[i])}

a(n) = {my(s=0); forpart(p=n, s+=permcount(p)*5^edges(p)); s/n!} \\ Andrew Howroyd, Oct 22 2017

CROSSREFS

Cf. A000595, A004105, A001374.

Sequence in context: A212041 A251696 A274306 * A085523 A292687 A152425

Adjacent sequences:  A053513 A053514 A053515 * A053517 A053518 A053519

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jan 14 2000

EXTENSIONS

a(9) from Andrew Howroyd, Oct 22 2017

STATUS

approved

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Last modified April 23 06:08 EDT 2019. Contains 322381 sequences. (Running on oeis4.)