A006202 Number of colorings of labeled graphs on n nodes using exactly 4 colors, divided by 4!*2^6.

0, 0, 0, 1, 80, 7040, 878080, 169967616, 53247344640, 27580935700480, 23884321532149760, 34771166607668412416, 85316631064301031915520, 353171748158258855521812480, 2467057266045387831319241687040, 29078599995993904385498084987109376

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Equals 1/1536*A224068. - Peter Bala, Apr 12 2013

References

• F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 18, col. 4 of Table 1.5.1 (divided by 64).
• R. C. Read, personal communication.
• 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 = 1..80
• R. C. Read, The number of k-colored graphs on labelled nodes, Canad. J. Math., 12 (1960), 410-414.
• R. C. Read, Letter to N. J. A. Sloane, Oct. 29, 1976

Crossrefs

A diagonal of A058875.

Cf. A000683, A224068.

Programs

Mathematica

maxn = 16;
t[, 1] = 1; t[n, k_] := t[n, k] = Sum[Binomial[n, j]*2^(j*(n - j))*t[j, k - 1]/k, {j, 1, n - 1}];
a[n_] := t[n, 4]/64;
Array[a, maxn]

PARI

seq(n)={Vec(serconvol(sum(j=1, n, x^j*j!*2^binomial(j,2)) + O(x*x^n), (sum(j=1, n, x^j/(j!*2^binomial(j,2))) + O(x*x^n))^4)/1536, -n)} \\ Andrew Howroyd, Nov 30 2018