OFFSET
0,2
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 232, # 3).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
G.f.: (1 + 9*x + 14*x^2 + 4*x^3)/(1 - x)^9.
a(n) = (n + 1)*(n + 2)^3*(n + 3)^2*(n + 4)*(n + 5)/1440 (from Maple section).
Sum_{n>=0} 1/a(n) = -240*zeta(3) + (400/3)*Pi^2 - 18475/18. - Jaume Oliver Lafont, Jul 10 2017
Sum_{n>=0} (-1)^n/a(n) = 4480*log(2)/3 + 180*zeta(3) - 20*Pi^2/3 - 21325/18. - Amiram Eldar, May 29 2022
MAPLE
a:=n->(n+1)*(n+2)^3*(n+3)^2*(n+4)*(n+5)/1440: seq(a(n), n=0..30);
MATHEMATICA
CoefficientList[Series[(1 + 9 x + 14 x^2 + 4 x^3) / (1 - x)^9, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 11 2017 *)
PROG
(Magma) [(n+1)*(n+2)^3*(n+3)^2*(n+4)*(n+5)/1440: n in [0..30]]; // Vincenzo Librandi, Jul 11 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 18 2005
STATUS
approved