A109124 a(n) = (n+1)*(n+2)^3*(n+3)^4*(n+4)^3*(n+5)*(2n+5)*(2n+7)/7257600.

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

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

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

Adjacent sequences: A109121 A109122 A109123 * A109125 A109126 A109127

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 20 2005

Status

approved