%I #16 Apr 22 2022 05:32:35

%S 0,0,72,1536,14400,92160,470400,2064384,8128512,29491200,100362240,

%T 324403200,1005109248,3005743104,8722022400,24662507520,68183654400,

%U 184817811456,492285984768,1291006771200,3338686955520,8526181171200,21526669688832,53788022931456

%N Number of copies of the star graph S(2,2,1) contained within the n-dimensional hypercube graph.

%C S(2,2,1) is the star graph with two legs of length two and one of length one.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (12,-60,160,-240,192,-64).

%F a(n) = (2^n)*(C(n,3))*(3n)*(n-2).

%F G.f.: 24*x^3*(3 + 28*x + 12*x^2)/(1 - 2*x)^6. - _Stefano Spezia_, Apr 15 2022

%F Sum_{n>=3} 1/a(n) = 13/32 + 3*log(2)^2/16 - log(2)/4 - Pi^2/32. - _Amiram Eldar_, Apr 22 2022

%t a[n_] := (2^n)*Binomial[n,3]*3*n*(n-2); Array[a, 24] (* _Amiram Eldar_, Apr 22 2022 *)

%o (Python) from math import comb

%o def a(n):

%o return (2**n)*comb(n,3)*3*n*(n-2)

%Y Cf. A129002, A352847.

%K easy,nonn

%O 1,3

%A _Ben Eck_, Apr 14 2022