A278704 Number of triangles in all simple labeled graphs on n nodes.

1, 32, 1280, 81920, 9175040, 1879048192, 721554505728, 527765581332480, 743093938516131840, 2029141848108050677760, 10804774512805748248936448, 112652543574969605015820304384, 2307124092415377510723999833784320, 93045959704944111103266494219624120320

Offset

3,2

Links

Table of n, a(n) for n=3..16.

Peter Maceli, Class Nine: Random Graphs

Formula

a(n) = binomial(n,3)*2^(binomial(n,2)-3).

a(n) = binomial(n,3)*(2^(n-3))^3*2^binomial(n-3,2). Geoffrey Critzer, Apr 13 2017

E.g.f.: x^3/3!*A(8x) where A(x) is the e.g.f. for A006125. Geoffrey Critzer, Apr 13 2017

Maple

A278704:=n->binomial(n, 3)*2^(binomial(n, 2)-3): seq(A278704(n), n=3..20); # Wesley Ivan Hurt, Jan 21 2017

Mathematica

Table[Binomial[n, 3] 2^(Binomial[n, 2] - 3), {n, 0, 15}]

Prog

(Magma) [Binomial(n, 3)*2^(Binomial(n, 2)-3): n in [3..20]]; // Vincenzo Librandi, Nov 27 2016

Crossrefs

Sequence in context: A247998 A208707 A038096 * A275141 A275036 A274732

Adjacent sequences: A278701 A278702 A278703 * A278705 A278706 A278707

Keyword

nonn,easy

Author

Geoffrey Critzer, Nov 26 2016

Status

approved