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 A038096 Number of rooted graphs on n labeled nodes where the root has degree 3. 5
 32, 1280, 61440, 4587520, 587202560, 135291469824, 57724360458240, 46443371157258240, 71337018097548656640, 211030752203237270487040, 1210134745434243803880882176, 13518305228996352601898436526080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 COMMENTS The graphs are not necessarily connected. The nodes are labeled. LINKS Andrew Howroyd, Table of n, a(n) for n = 4..50 FORMULA a(n) = n*binomial(n-1,3)*2^binomial(n-1,2). (There are n choices for the root, binomial(n-1,3) choices for the nodes it joined to, and 2^binomial(n-1,2) choices for the edges between the non-root nodes.) EXAMPLE For n=4, take 4 nodes labeled a,b,c,d. We can choose the root in 4 ways, say a, and it must be joined to b,c,d. Each of the three edges bc, bd, cd may or may not exist, so there are 4*8 = 32 = a(4) possibilities. MATHEMATICA Table[n Binomial[n-1, 3] 2^Binomial[n-1, 2], {n, 4, 20}] (* Harvey P. Dale, Sep 14 2011 *) PROG (PARI) a(n) = {n*binomial(n-1, 3)*2^binomial(n-1, 2)} \\ Andrew Howroyd, Nov 23 2020 CROSSREFS Cf. A006125, A038094, A038095, A038097. Sequence in context: A248072 A247998 A208707 * A278704 A275141 A275036 Adjacent sequences:  A038093 A038094 A038095 * A038097 A038098 A038099 KEYWORD nonn,easy,changed AUTHOR Christian G. Bower, Jan 04 1999 EXTENSIONS Edited by N. J. A. Sloane, Sep 14 2011 STATUS approved

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Last modified November 24 07:53 EST 2020. Contains 338607 sequences. (Running on oeis4.)