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A278736
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Number of size-4 cliques in all simple labeled graphs on n nodes.
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1
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1, 80, 7680, 1146880, 293601280, 135291469824, 115448720916480, 185773484629032960, 570696144780389253120, 3376492035251796327792640, 38724311853895801724188229632, 865171534655766566521499937669120
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OFFSET
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4,2
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LINKS
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FORMULA
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a(n) = binomial(n,4)*2^(binomial(n,2)-6).
The number of size p cliques in all simple labeled graphs is binomial(n,p)*2^(binomial(n,2)-binomial(p,2).
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EXAMPLE
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a(6) = binomial(6,4)*2^(binomial(6,2)-6) = 15 * 2^(15-6) = 15 * (2^9) = 7680. - Indranil Ghosh, Feb 25 2017
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MATHEMATICA
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Table[Binomial[n, 4] 2^(Binomial[n, 2] - 6), {n, 4, 15}]
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PROG
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(PARI) a(n) = binomial(n, 4)*2^(binomial(n, 2)-6) \\ Indranil Ghosh, Feb 25 2017
(Python)
import math
f=math.factorial
def C(n, r): return f(n)/f(r)/f(n-r)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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