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A109124
a(n) = (n+1)*(n+2)^3*(n+3)^4*(n+4)^3*(n+5)*(2n+5)*(2n+7)/7257600.
1
1, 90, 2475, 35035, 321048, 2159136, 11511720, 51210225, 196994655, 672567610, 2078241165, 5900460930, 15576433600, 38599672320, 90491328576, 201987412398, 431582100885, 886725689850, 1758635878615, 3378012822261, 6302164837320, 11448416980000, 20294512875000
OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids.
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 186, D(4,5,n)).
LINKS
Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
FORMULA
G.f.: (1+x)(1 + 74x + 1156x^2 + 5749x^3 + 10064x^4 + 5749x^5 + 1156x^6 + 74x^7 + x^8)/(1-x)^15.
From Amiram Eldar, May 31 2022: (Start)
Sum_{n>=0} 1/a(n) = 63344246/3 - 1940400*Pi^2 - 20160*Pi^4.
Sum_{n>=0} (-1)^n/a(n) = 18350080*Pi - 1222200*Pi^2 - 17640*Pi^4 - 131602646/3. (End)
MAPLE
a:=n->(n+1)*(n+2)^3*(n+3)^4*(n+4)^3*(n+5)*(2*n+5)*(2*n+7)/7257600: seq(a(n), n=0..23);
MATHEMATICA
Table[((n+1)(n+2)^3 (n+3)^4 (n+4)^3 (n+5)(2n+5)(2n+7))/7257600, {n, 0, 30}] (* Harvey P. Dale, Sep 04 2020 *)
CROSSREFS
Sequence in context: A008393 A055603 A210090 * A013359 A013355 A013357
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 20 2005
STATUS
approved