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%I A352994 #16 Apr 22 2022 05:32:35
%S A352994 0,0,72,1536,14400,92160,470400,2064384,8128512,29491200,100362240,
%T A352994 324403200,1005109248,3005743104,8722022400,24662507520,68183654400,
%U A352994 184817811456,492285984768,1291006771200,3338686955520,8526181171200,21526669688832,53788022931456
%N A352994 Number of copies of the star graph S(2,2,1) contained within the n-dimensional hypercube graph.
%C A352994 S(2,2,1) is the star graph with two legs of length two and one of length one.
%H A352994 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (12,-60,160,-240,192,-64).
%F A352994 a(n) = (2^n)*(C(n,3))*(3n)*(n-2).
%F A352994 G.f.: 24*x^3*(3 + 28*x + 12*x^2)/(1 - 2*x)^6. - _Stefano Spezia_, Apr 15 2022
%F A352994 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 A352994 a[n_] := (2^n)*Binomial[n,3]*3*n*(n-2); Array[a, 24] (* _Amiram Eldar_, Apr 22 2022 *)
%o A352994 (Python) from math import comb
%o A352994 def a(n):
%o A352994     return (2**n)*comb(n,3)*3*n*(n-2)
%Y A352994 Cf. A129002, A352847.
%K A352994 easy,nonn
%O A352994 1,3
%A A352994 _Ben Eck_, Apr 14 2022

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