This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A006201 M5167 #34 May 10 2025 23:14:20
%S A006201 0,0,1,24,640,24000,1367296,122056704,17282252800,3897054412800,
%T A006201 1400795928395776,802530102499344384,732523556206878392320,
%U A006201 1064849635418836398243840,2464403435614136308036796416
%N A006201 Number of colorings of labeled graphs on n nodes using exactly 3 colors, divided by 48.
%C A006201 Equals 1/48*A213442. - _Peter Bala_, Apr 12 2013
%D A006201 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 18, table 1.5.1, column 3 (divided by 8).
%D A006201 R. C. Read, personal communication.
%D A006201 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006201 Alois P. Heinz, <a href="/A006201/b006201.txt">Table of n, a(n) for n = 1..75</a>
%H A006201 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 A006201 R. C. Read, <a href="/A000684/a000684_1.pdf">Letter to N. J. A. Sloane, Oct. 29, 1976</a>
%F A006201 Let E(x) = sum {n >= 0} x^n/(n!*2^C(n,2)) = 1 + x + x^2/(2!*2) + x^3/(3!*2^3) + x^4/(4!*2^6) + .... Then a generating function is 1/48*(E(x) - 1)^3 = x^3/(3!*2^3) + 24*x^4/(4!*2^6) + 640*x^6/(5!*2^10) + ... (see Read). - _Peter Bala_, Apr 12 2013
%t A006201 F2[n_] := Sum[Binomial[n, r]*2^(r*(n-r)), {r, 1, n-1}]; F3[n_] := Sum[Binomial[n, r]*2^(r*(n-r))*F2[r], {r, 1, n-1}]; a[n_] := F3[n]/48; Table[a[n], {n, 1, 15}] (* _Jean-François Alcover_, Mar 06 2014, after Maple code in A213442 *)
%o A006201 (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))^3)/48, -n)} \\ _Andrew Howroyd_, Nov 30 2018
%Y A006201 Cf. A000683. A diagonal of A058843. A213442.
%K A006201 nonn,easy,nice
%O A006201 1,4
%A A006201 _N. J. A. Sloane_
%E A006201 More terms from _Vladeta Jovovic_, Feb 03 2000