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%I #16 Apr 14 2017 03:42:28
%S 1,80,7680,1146880,293601280,135291469824,115448720916480,
%T 185773484629032960,570696144780389253120,3376492035251796327792640,
%U 38724311853895801724188229632,865171534655766566521499937669120
%N Number of size-4 cliques in all simple labeled graphs on n nodes.
%H Indranil Ghosh, <a href="/A278736/b278736.txt">Table of n, a(n) for n = 4..80</a>
%F a(n) = binomial(n,4)*2^(binomial(n,2)-6).
%F The number of size p cliques in all simple labeled graphs is binomial(n,p)*2^(binomial(n,2)-binomial(p,2).
%F E.g.f.: x^4/4!*A(16x) where A(x) is the e.g.f. for A006125. - _Geoffrey Critzer_, Apr 13 2017
%e a(6) = binomial(6,4)*2^(binomial(6,2)-6) = 15 * 2^(15-6) = 15 * (2^9) = 7680. - _Indranil Ghosh_, Feb 25 2017
%t Table[Binomial[n, 4] 2^(Binomial[n, 2] - 6), {n, 4, 15}]
%o (PARI) a(n) = binomial(n,4)*2^(binomial(n,2)-6) \\ _Indranil Ghosh_, Feb 25 2017
%o (Python)
%o import math
%o f=math.factorial
%o def C(n,r): return f(n)/f(r)/f(n-r)
%o def A278736(n): return C(n,4)*2**(C(n,2)-6) # _Indranil Ghosh_, Feb 25 2017
%Y Cf. A278704, A278705.
%K nonn
%O 4,2
%A _Geoffrey Critzer_, Nov 27 2016
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