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

%I A006202 M5356 #29 May 10 2025 23:14:51
%S A006202 0,0,0,1,80,7040,878080,169967616,53247344640,27580935700480,
%T A006202 23884321532149760,34771166607668412416,85316631064301031915520,
%U A006202 353171748158258855521812480,2467057266045387831319241687040,29078599995993904385498084987109376
%N A006202 Number of colorings of labeled graphs on n nodes using exactly 4 colors, divided by 4!*2^6.
%C A006202 Equals 1/1536*A224068. - _Peter Bala_, Apr 12 2013
%D A006202 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 18, col. 4 of Table 1.5.1 (divided by 64).
%D A006202 R. C. Read, personal communication.
%D A006202 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006202 Andrew Howroyd, <a href="/A006202/b006202.txt">Table of n, a(n) for n = 1..80</a>
%H A006202 R. C. Read, <a href="http://cms.math.ca/10.4153/CJM-1960-035-0">The number of k-colored graphs on labelled nodes</a>, Canad. J. Math., 12 (1960), 410-414.
%H A006202 R. C. Read, <a href="/A000684/a000684_1.pdf">Letter to N. J. A. Sloane, Oct. 29, 1976</a>
%t A006202 maxn = 16;
%t A006202 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}];
%t A006202 a[n_] := t[n, 4]/64;
%t A006202 Array[a, maxn]
%o A006202 (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
%Y A006202 A diagonal of A058875.
%Y A006202 Cf. A000683, A224068.
%K A006202 nonn,easy
%O A006202 1,5
%A A006202 _N. J. A. Sloane_