

A002032


Number of ncolored connected graphs on n labeled nodes.
(Formerly M2141 N0852)


6



1, 1, 2, 24, 912, 87360, 19226880, 9405930240, 10142439229440, 24057598104207360, 125180857812868300800, 1422700916050060841779200, 35136968950395142864227532800, 1876028272361273394915958613606400, 215474119792145796020405035320528076800
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OFFSET

0,3


COMMENTS

Every connected graph on n nodes can be colored with n colors in exactly n! ways, so this sequence is just n! * A001187(n).  Andrew Howroyd, Dec 03 2018


REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS



FORMULA

Define M_0(k)=1, M_n(0)=0, M_n(k) = Sum_{r=0..n} C(n,r)*2^(r*(nr))*M_r(k1) [M_n(k) = A322280(n,k)], m_n(k) = M_n(k) Sum_{r=1..n1} C(n1,r1)*m_r(k)*M_{nr}(k) [m_n(k) = A322279(n,k)], f_n(k) = Sum_{r=1..k} (1)^(kr)*C(k,r)*m_n(r). This sequence gives a(n) = f_n(n).  Sean A. Irvine, May 29 2013, edited Andrew Howroyd, Dec 03 2018


MATHEMATICA

(* b = A001187 *) b[n_] := b[n] = If[n == 0, 1, 2^(n(n1)/2)  Sum[k* Binomial[n, k]*2^((nk)(nk1)/2)*b[k], {k, 1, n1}]/n];
a[n_] := n! b[n];


PROG

(PARI) seq(n) = {Vec(serlaplace(serlaplace(1 + log(sum(k=0, n, 2^binomial(k, 2)*x^k/k!, O(x*x^n))))))} \\ Andrew Howroyd, Dec 03 2018


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



