OFFSET
0,2
REFERENCES
R. C. Read, personal communication.
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
Andrew Howroyd, Table of n, a(n) for n = 0..50
R. C. Read, E. M. Wright, Colored graphs: A correction and extension, Canad. J. Math. 22 1970 594-596.
FORMULA
E.g.f.: log(A(x))+1 where A(x) is the e.g.f. for A191371. - Geoffrey Critzer, Jun 02 2011
a(n) = m_n(3) using the functions defined in A002032. - Sean A. Irvine, May 29 2013
Logarithmic transform of A191371. - Andrew Howroyd, Dec 03 2018
MATHEMATICA
f[{k_, r_, m_}]:= Binomial[m+r+k, k] Binomial[m+r, r] 2^(k r +k m + r m);
a = Sum[Total[Map[f, Compositions[n, 3]]] x^n/n!, {n, 0, 20}];
Range[0, 20]! CoefficientList[Series[Log[a]+1, {x, 0, 20}], x] (* Geoffrey Critzer, Jun 02 2011 *)
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))^3))))} \\ Andrew Howroyd, Dec 03 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved