A006202 Number of colorings of labeled graphs on n nodes using exactly 4 colors, divided by 4!*2^6. (Formerly M5356)

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

Offset

1,5

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

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]

Prog

(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

Crossrefs

A diagonal of A058875.

Cf. A000683, A224068.

Sequence in context: A259076 A335610 A190931 * A278736 A116252 A159734

Adjacent sequences: A006199 A006200 A006201 * A006203 A006204 A006205

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved