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%I #35 Feb 05 2022 16:41:59
%S 1,11,56,196,546,1302,2772,5412,9867,17017,28028,44408,68068,101388,
%T 147288,209304,291669,399399,538384,715484,938630,1216930,1560780,
%U 1981980,2493855,3111381,3851316,4732336,5775176,7002776,8440432
%N Expansion of g.f.: (1+4*x)/(1-x)^7.
%C Kekulé numbers for certain benzenoids. - _Emeric Deutsch_, Jun 18 2005
%C Equals row sums of triangle A143130, and binomial transform of {1, 10, 35, 60, 55, 26, 5, 0, 0, 0, ...}. - _Gary W. Adamson_, Jul 27 2008
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%D S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p.233, # 5).
%H Vincenzo Librandi, <a href="/A051946/b051946.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n) = binomial(n+5,5)*(5*n+6)/6.
%F a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(5*n+6)/720. - _Emeric Deutsch_, Jun 18 2005
%F a(n) = A034264(n+1). - _R. J. Mathar_, Oct 14 2008
%p a:=n->(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(5*n+6)/720: seq(a(n),n=0..35); # _Emeric Deutsch_
%t CoefficientList[Series[(1+4x)/(1-x)^7, {x, 0, 40}], x] (* _Vincenzo Librandi_, Jul 30 2014 *)
%o (Magma) [(5*n+6)*Binomial(n+5,5)/6: n in [0..40]]; // _Vincenzo Librandi_, Jul 30 2014
%o (PARI) vector(40, n, (5*n+1)*binomial(n+4,5)/6) \\ _G. C. Greubel_, Aug 28 2019
%o (Sage) [(5*n+6)*binomial(n+5,5)/6 for n in (0..40)] # _G. C. Greubel_, Aug 28 2019
%o (GAP) List([0..40], n-> (5*n+6)*Binomial(n+5,5)/6); # _G. C. Greubel_, Aug 28 2019
%Y Partial sums of A027800.
%Y Cf. A093562 ((5, 1) Pascal, column m=6).
%Y Cf. A143130.
%Y Cf. similar sequences listed in A254142.
%K nonn,easy
%O 0,2
%A _Barry E. Williams_, Dec 20 1999
%E Corrected and extended by _Emeric Deutsch_, Jun 18 2005
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