A278736 Number of size-4 cliques in all simple labeled graphs on n nodes.

1, 80, 7680, 1146880, 293601280, 135291469824, 115448720916480, 185773484629032960, 570696144780389253120, 3376492035251796327792640, 38724311853895801724188229632, 865171534655766566521499937669120

Offset

4,2

Links

Indranil Ghosh, Table of n, a(n) for n = 4..80

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

Cf. A278704, A278705.

Sequence in context: A335610 A190931 A006202 * A116252 A159734 A091754

Adjacent sequences: A278733 A278734 A278735 * A278737 A278738 A278739

Keyword

nonn,easy

Author

Geoffrey Critzer, Nov 27 2016

Status

approved