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A107916
a(n) = binomial(n+3,2)*binomial(n+4,3)*binomial(n+5,5)/12.
1
1, 30, 350, 2450, 12348, 49392, 166320, 490050, 1297725, 3149146, 7105098, 15071420, 30321200, 58262400, 107535744, 191548044, 330569505, 554550150, 906840550, 1449035742, 2267198780, 3479762000, 5247450000, 7785618750, 11379460365, 16402583106, 23339541330
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. 229).
LINKS
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
a(n) = (1/17280)(n+1)(n+2)^3*(n+3)^3*(n+4)^2*(n+5).
G.f.: -(2*x^5+28*x^4+85*x^3+75*x^2+19*x+1)/(x-1)^11. - Colin Barker, Sep 20 2012
From Amiram Eldar, May 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 1400*Pi^2 + 2880*zeta(3) - 51835/3.
Sum_{n>=0} (-1)^n/a(n) = 20*Pi^2 + 28160*log(2) + 4320*zeta(3) - 74725/3. (End)
MAPLE
a:=n->(1/12)*binomial(n+3, 2)*binomial(n+4, 3)*binomial(n+5, 5): seq(a(n), n=0..30);
MATHEMATICA
a[n_] := Binomial[n + 3, 2] * Binomial[n + 4, 3] * Binomial[n + 5, 5]/12; Array[a, 25, 0] (* Amiram Eldar, May 29 2022 *)
CROSSREFS
Sequence in context: A214085 A125418 A339197 * A091775 A222086 A008656
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 12 2005
STATUS
approved