A108645 a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)*(2*n^2 + 6*n + 5)/720.

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

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

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

Cf. A108646, A108647, A108648, A108649, A108650.

Sequence in context: A088889 A348490 A060105 * A086023 A296539 A229715

Adjacent sequences: A108642 A108643 A108644 * A108646 A108647 A108648

Keyword

nonn

Author

Emeric Deutsch, Jun 13 2005

Status

approved