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A278736
Number of size-4 cliques in all simple labeled graphs on n nodes.
1
1, 80, 7680, 1146880, 293601280, 135291469824, 115448720916480, 185773484629032960, 570696144780389253120, 3376492035251796327792640, 38724311853895801724188229632, 865171534655766566521499937669120
OFFSET
4,2
LINKS
FORMULA
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)).
E.g.f.: x^4/4!*A(16x) where A(x) is the e.g.f. for A006125. - Geoffrey Critzer, Apr 13 2017
EXAMPLE
a(6) = binomial(6,4)*2^(binomial(6,2)-6) = 15 * 2^(15-6) = 15 * (2^9) = 7680. - Indranil Ghosh, Feb 25 2017
MATHEMATICA
Table[Binomial[n, 4] 2^(Binomial[n, 2] - 6), {n, 4, 15}]
PROG
(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)
def A278736(n): return C(n, 4)*2**(C(n, 2)-6) # Indranil Ghosh, Feb 25 2017
CROSSREFS
Sequence in context: A335610 A190931 A006202 * A116252 A159734 A091754
KEYWORD
nonn,easy
AUTHOR
Geoffrey Critzer, Nov 27 2016
STATUS
approved