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A352847
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Number of copies of the star graph S(2,1,1) contained within the n-dimensional hypercube graph.
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3
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0, 0, 48, 576, 3840, 19200, 80640, 301056, 1032192, 3317760, 10137600, 29736960, 84344832, 232587264, 626196480, 1651507200, 4278190080, 10909384704, 27433893888, 68136468480, 167352729600, 406931374080, 980510834688, 2343038877696, 5556613939200
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OFFSET
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1,3
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COMMENTS
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The star graph S(2,1,1) is the unique tree with degree sequence 3,2,1,1,1.
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LINKS
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FORMULA
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a(n) = 2^n*binomial(n,2)*(n-1)*(n-2).
Sum_{n>=3} 1/a(n) = 9/8 + log(2)^2/2 - 3*log(2)/4 - Pi^2/12. - Amiram Eldar, Apr 22 2022
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MATHEMATICA
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a[n_] := (2^n)*Binomial[n, 2]*(n-1)*(n-2); Array[a, 25] (* Amiram Eldar, Apr 22 2022 *)
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PROG
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(Python) from math import comb
def a(n):
return (2**n)*comb(n, 2)*(n-2)*(n-1)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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