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
Keywords
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).
Programs
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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
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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);
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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 *) -
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
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
Comments