A107943 a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)^2*(n+5)*(2n+3)/8640.

1, 25, 245, 1470, 6468, 22932, 69300, 185130, 448305, 1002001, 2095093, 4140500, 7796880, 14080080, 24511824, 41314284, 67660425, 107991345, 168413245, 257188162, 385334180, 567352500, 822100500, 1173831750, 1653425865

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

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

G.f.: (1+15*x+40*x^2+25*x^3+3*x^4)/(1-x)^10. - Bruno Berselli, Apr 19 2011

From Amiram Eldar, May 31 2022: (Start)

Sum_{n>=0} 1/a(n) = 264*Pi^2 - 49152*log(2)/35 - 57089/35.

Sum_{n>=0} (-1)^n/a(n) = 12288*Pi/35 - 12*Pi^2 + 13824*log(2)/35 - 44007/35. (End)

Maple

a:=n->(1/8640)*(n+1)*(n+2)^2*(n+3)^2*(n+4)^2*(n+5)*(2*n+3): seq(a(n), n=0..30);

Mathematica

Table[((n+1)(n+2)^2(n+3)^2(n+4)^2(n+5)(2n+3))/8640, {n, 0, 30}]  (* Harvey P. Dale, Apr 19 2011 *)

Crossrefs

Sequence in context: A294290 A352304 A362393 * A125388 A126546 A023073

Adjacent sequences: A107940 A107941 A107942 * A107944 A107945 A107946

Keyword

nonn

Author

Emeric Deutsch, Jun 12 2005

Status

approved