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%I #33 May 10 2020 13:47:26
%S 1,1,4,1,24,48,1,160,1152,1536,1,1440,30720,122880,122880,1,18304,
%T 1152000,10813440,29491200,23592960,1,330624,65630208,1348730880,
%U 7707033600,15854469120,10569646080,1,8488960,5858721792,261070258176,2853804441600,11499774935040,18940805775360,10823317585920
%N Triangle giving a(n,k) = number of k-colored labeled graphs with n nodes.
%H Alois P. Heinz, <a href="/A046860/b046860.txt">Rows n = 1..50, flattened</a>
%H 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.
%F a(n, k) = Sum_{r=1..n-1} C(n, r) 2^(r*(n-r)) a(r, k-1).
%F 1 + Sum_{n>=1} Sum_{k=1..n} a(n,k)*y^k*x^n/(n!*2^C(n,2)) = 1/(1-y(E(x)-1)) where E(x) = Sum_{n>=0} x^n/(n!*2^C(n,2)). - _Geoffrey Critzer_, May 06 2020
%e Triangle begins:
%e 1;
%e 1, 4;
%e 1, 24, 48;
%e 1, 160, 1152, 1536;
%e 1, 1440, 30720, 122880, 122880;
%e 1, 18304, 1152000, 10813440, 29491200, 23592960;
%e ...
%p a:= proc(n, k) option remember; `if`([n, k]=[0$2], 1,
%p add(binomial(n, r)*2^(r*(n-r))*a(r, k-1), r=0..n-1))
%p end:
%p seq(seq(a(n,k), k=1..n), n=1..8); # _Alois P. Heinz_, Apr 21 2020
%t a[n_ /; n >= 1, k_ /; k >= 1] := a[n, k] = Sum[ Binomial[n, r]*2^(r*(n - r))*a[r, k - 1], {r, 1, n - 1}]; a[_, 0] = 1; Flatten[ Table[ a[n, k], {n, 1, 8}, {k, 0, n - 1}]] (* _Jean-François Alcover_, Dec 12 2011, after formula *)
%Y Column #1 gives A000683.
%Y Main diagonal gives A011266.
%Y Row sums give A334282.
%Y Cf. A000683, A006201, A006202.
%K tabl,easy,nice,nonn
%O 1,3
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Feb 04 2000
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