A107916 a(n) = binomial(n+3,2)*binomial(n+4,3)*binomial(n+5,5)/12.

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

T. D. Noe, Table of n, a(n) for n = 0..1000

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

Adjacent sequences: A107913 A107914 A107915 * A107917 A107918 A107919

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 12 2005

Status

approved