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A108645
a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)*(2*n^2 + 6*n + 5)/720.
4
1, 26, 250, 1435, 5978, 19992, 56952, 143550, 328515, 695266, 1379378, 2591953, 4650100, 8015840, 13344864, 21546684, 33857829, 51929850, 77934010, 114684647, 165783310, 235785880, 330395000, 456680250, 623328615, 840927906, 1122285906
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. 21).
LINKS
FORMULA
G.f.: (1+17*x+52*x^2+37*x^3+5*x^4)/(1-x)^9. - Harvey P. Dale, Sep 05 2016
E.g.f.: (1/6!)*(720 + 18000*x + 71640*x^2 + 91440*x^3 + 49050*x^4 + 12486*x^5 + 1565*x^6 + 92*x^7 + 2*x^8)*exp(x). - G. C. Greubel, Oct 19 2023
MAPLE
a:=(n+1)*(n+2)^2*(n+3)^2*(n+4)*(2*n^2+6*n+5)/720: seq(a(n), n=0..30);
MATHEMATICA
Table[(n+1)(n+2)^2(n+3)^2(n+4)(2n^2+6n+5)/720, {n, 0, 30}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 26, 250, 1435, 5978, 19992, 56952, 143550, 328515}, 30] (* Harvey P. Dale, Sep 05 2016 *)
PROG
(Magma) B:=Binomial; [(2*n^2+6*n+5)*B(n+4, 4)*B(n+3, 2)/15: n in [0..40]]; // G. C. Greubel, Oct 19 2023
(SageMath) b=binomial; [(2*n^2+6*n+5)*b(n+4, 4)*b(n+3, 2)/15 for n in range(41)] # G. C. Greubel, Oct 19 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jun 13 2005
STATUS
approved