A352847 - OEIS

%I #16 Apr 22 2022 04:39:29

%S 0,0,48,576,3840,19200,80640,301056,1032192,3317760,10137600,29736960,

%T 84344832,232587264,626196480,1651507200,4278190080,10909384704,

%U 27433893888,68136468480,167352729600,406931374080,980510834688,2343038877696,5556613939200

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

%C The star graph S(2,1,1) is the unique tree with degree sequence 3,2,1,1,1.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (10,-40,80,-80,32).

%F a(n) = 2^n*binomial(n,2)*(n-1)*(n-2).

%F G.f.: 48*x^3*(1 + 2*x)/(1 - 2*x)^5. - _Stefano Spezia_, Apr 15 2022

%F Sum_{n>=3} 1/a(n) = 9/8 + log(2)^2/2 - 3*log(2)/4 - Pi^2/12. - _Amiram Eldar_, Apr 22 2022

%t a[n_] := (2^n)*Binomial[n,2]*(n-1)*(n-2); Array[a, 25] (* _Amiram Eldar_, Apr 22 2022 *)

%o (Python) from math import comb

%o def a(n):

%o     return (2**n)*comb(n,2)*(n-2)*(n-1)

%Y Cf. A129002.

%K nonn,easy

%O 1,3

%A _Ben Eck_, Apr 05 2022