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A108648 a(n) = (n+1)^2*(n+2)^3*(n+3)/24. 5
1, 18, 120, 500, 1575, 4116, 9408, 19440, 37125, 66550, 113256, 184548, 289835, 441000, 652800, 943296, 1334313, 1851930, 2527000, 3395700, 4500111, 5888828, 7617600, 9750000, 12358125, 15523326, 19336968, 23901220, 29329875, 35749200 (list; graph; refs; listen; history; text; internal format)
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. 230, no. 24).
LINKS
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 230, no. 24).
FORMULA
From Colin Barker, Apr 22 2020: (Start)
G.f.: (1 + 11*x + 15*x^2 + 3*x^3) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>6.
(End)
a(n) = A000217(n+1) * A002415(n+2). - J. M. Bergot, May 21 2022
From Amiram Eldar, May 28 2022: (Start)
Sum_{n>=0} 1/a(n) = 24*zeta(3) + 6*Pi^2 - 87.
Sum_{n>=0} (-1)^n/a(n) = 99 - Pi^2 - 96*log(2) - 18*zeta(3). (End)
E.g.f.: (24 + 408*x + 1020*x^2 + 772*x^3 + 224*x^4 + 26*x^5 + x^6)*exp(x)/4!. - G. C. Greubel, Oct 28 2022
MAPLE
a:=(n+1)^2*(n+2)^3*(n+3)/24: seq(a(n), n=0..36);
MATHEMATICA
Table[(n+1)^2*(n+2)^3*(n+3)/24, {n, 0, 30}] (* G. C. Greubel, Oct 28 2022 *)
PROG
(PARI) Vec((1 + 11*x + 15*x^2 + 3*x^3) / (1 - x)^7 + O(x^30)) \\ Colin Barker, Apr 22 2020
(Magma) [(n+1)^2*(n+2)^3*(n+3)/24: n in [0..30]]; // G. C. Greubel, Oct 28 2022
(SageMath) [(n+1)^2*(n+2)^3*(n+3)/24 for n in (0..30)] # G. C. Greubel, Oct 28 2022
CROSSREFS
Cf. A108647.
Sequence in context: A044350 A044731 A190705 * A264360 A223046 A037064
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 13 2005
STATUS
approved

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Last modified March 29 08:00 EDT 2024. Contains 371265 sequences. (Running on oeis4.)