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A006712
Number of 3-edge-colored trivalent graphs with 2n labeled nodes.
(Formerly M4311)
6
6, 480, 197820, 150474240, 208857587400, 471804812519040, 1625459273858019600, 8112729590064978278400, 56342429224416522460072800, 527075322501595757416502976000, 6466573585901882433727764077860800, 101749747195531624711768653503416320000
OFFSET
2,1
REFERENCES
R. C. Read, Some Enumeration Problems in Graph Theory. Ph.D. Dissertation, Department of Mathematics, Univ. London, 1958.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. C. Read, Letter to N. J. A. Sloane, Feb 04 1971 (gives initial terms of this sequence)
PROG
(PARI)
dpermcount(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*=2*t*k; s+=2*t); s!/m}
S(n, x)={vector(n, n, if(n>1, sum(k=0, n, binomial(2*n-k, k)*2*n/(2*n-k)*x^k), 0))}
q(n, s)={my(t=0); if(n>1, forpart(p=n, t+=dpermcount(p)*prod(i=1, #p, s[p[i]]), [2, n])); t}
a(n)={my(p=q(n, S(n, x))); sum(i=0, poldegree(p), polcoeff(p, n-i)*(-1)^(n-i)*(2*i)!/(2^i*i!))} \\ Andrew Howroyd, Dec 18 2017
CROSSREFS
Cf. A006713 (for connected cases), A248361 (for the incorrect values). See also A002830, A002831, A005638.
Sequence in context: A318634 A006713 A248362 * A248361 A345027 A203428
KEYWORD
nonn
EXTENSIONS
a(5)-a(6) corrected and a(7)-a(10) from Sean A. Irvine, Oct 05 2014
Terms a(11) and beyond from Andrew Howroyd, Dec 18 2017
STATUS
approved