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A352847 Number of copies of the star graph S(2,1,1) contained within the n-dimensional hypercube graph. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
The star graph S(2,1,1) is the unique tree with degree sequence 3,2,1,1,1.
LINKS
FORMULA
a(n) = 2^n*binomial(n,2)*(n-1)*(n-2).
G.f.: 48*x^3*(1 + 2*x)/(1 - 2*x)^5. - Stefano Spezia, Apr 15 2022
Sum_{n>=3} 1/a(n) = 9/8 + log(2)^2/2 - 3*log(2)/4 - Pi^2/12. - Amiram Eldar, Apr 22 2022
MATHEMATICA
a[n_] := (2^n)*Binomial[n, 2]*(n-1)*(n-2); Array[a, 25] (* Amiram Eldar, Apr 22 2022 *)
PROG
(Python) from math import comb
def a(n):
return (2**n)*comb(n, 2)*(n-2)*(n-1)
CROSSREFS
Cf. A129002.
Sequence in context: A266210 A245953 A192832 * A042949 A190601 A179404
KEYWORD
nonn,easy
AUTHOR
Ben Eck, Apr 05 2022
STATUS
approved

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Last modified April 13 15:38 EDT 2024. Contains 371644 sequences. (Running on oeis4.)