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A002029
Number of connected graphs on n labeled nodes, each node being colored with one of 4 colors, such that no edge joins nodes of the same color.
(Formerly M3459 N1406)
3
1, 4, 12, 132, 3156, 136980, 10015092, 1199364852, 234207001236, 75018740661780, 39745330657406772, 35073541377640231092, 51798833078501480220756, 128412490016744675540378580, 535348496386845235339961362932, 3757366291145650829115977555259252
OFFSET
0,2
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).
R. C. Read, personal communication.
LINKS
R. C. Read, E. M. Wright, Colored graphs: A correction and extension, Canad. J. Math. 22 1970 594-596.
FORMULA
E.g.f.: log(b(x)+1)+1 where b(x) = 4 * e.g.f. of A000686. - Sean A. Irvine, May 27 2013
a(n) = m_n(4) using the functions defined in A002032. - Sean A. Irvine, May 29 2013
Logarithmic transform of A223887. - Andrew Howroyd, Dec 03 2018
MATHEMATICA
m = 16;
serconv = (CoefficientList[Sum[x^j*2^Binomial[j, 2], {j, 0, m}] + O[x]^m, x]*CoefficientList[(Sum[x^j/(j!*2^Binomial[j, 2]), {j, 0, m}] + O[x]^m)^4, x]) . x^Range[0, m-1];
CoefficientList[1 + Log[serconv] + O[x]^m, x]*Range[0, m-1]! (* Jean-François Alcover, Sep 04 2019, after Andrew Howroyd *)
PROG
(PARI) seq(n)={Vec(serlaplace(1 + log(serconvol(sum(j=0, n, x^j*2^binomial(j, 2)) + O(x*x^n), (sum(j=0, n, x^j/(j!*2^binomial(j, 2))) + O(x*x^n))^4))))} \\ Andrew Howroyd, Dec 03 2018
CROSSREFS
Column k=4 of A322279.
Cf. A002032.
Sequence in context: A053551 A009663 A197899 * A204321 A152121 A077611
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, May 27 2013
Name clarified and offset corrected by Andrew Howroyd, Dec 03 2018
STATUS
approved