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A199840 Triangle read by rows: T(n,k) is the number of 2-multigraphs on n nodes having exactly k edges, with n >= 1 and 0 <= k <= n*(n-1). 1
1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 3, 5, 8, 9, 12, 9, 8, 5, 3, 1, 1, 1, 1, 3, 6, 14, 24, 43, 62, 87, 100, 110, 100, 87, 62, 43, 24, 14, 6, 3, 1, 1, 1, 1, 3, 7, 18, 40, 91, 180, 352, 616, 1006, 1483, 2036, 2522, 2891, 3012, 2891, 2522, 2036, 1483, 1006, 616, 352, 180, 91, 40, 18, 7, 3, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Here a 2-multigraph is an unlabeled graph with at most 2 edges connecting any vertex pair with no self loops allowed.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..2680 (first 20 rows)

EXAMPLE

Triangle begins:

  1;

  1, 1, 1;

  1, 1, 2, 2, 2, 1, 1;

  1, 1, 3, 5, 8, 9, 12, 9, 8, 5, 3, 1, 1;

  ...

MATHEMATICA

Table[CoefficientList[Expand[PairGroupIndex[SymmetricGroup[n], s] /. Table[s[i]->1+x^i+x^(2i), {i, 1, Binomial[n, 2]}]], x], {n, 1, 6}]

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)^g )) * prod(i=1, #v, my(c=v[i]); t(c)^((c-1)\2)*if(c%2, 1, t(c/2)))}

Row(n) = {my(s=0); forpart(p=n, s+=permcount(p)*edges(p, i->1+x^i+(x^2)^i)); Vecrev(s/n!)}

{ for(n=1, 6, print(Row(n))) } \\ Andrew Howroyd, Nov 07 2019

CROSSREFS

Row sums are A004102.

Cf. A008406.

Sequence in context: A073426 A232439 A309797 * A126067 A327490 A238408

Adjacent sequences:  A199837 A199838 A199839 * A199841 A199842 A199843

KEYWORD

nonn,tabf

AUTHOR

Geoffrey Critzer, Nov 11 2011

EXTENSIONS

Terms a(46) and beyond from Andrew Howroyd, Nov 07 2019

STATUS

approved

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Last modified April 3 17:03 EDT 2020. Contains 333197 sequences. (Running on oeis4.)