OFFSET
1,3
COMMENTS
The star graph S(2,1,1) is the unique tree with degree sequence 3,2,1,1,1.
LINKS
Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).
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
KEYWORD
nonn,easy
AUTHOR
Ben Eck, Apr 05 2022
STATUS
approved