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A113335 a(n) = 3^5 * binomial(n+4, 5).

%I A113335 #15 Aug 29 2022 04:39:51
%S A113335 243,1458,5103,13608,30618,61236,112266,192456,312741,486486,729729,
%T A113335 1061424,1503684,2082024,2825604,3767472,4944807,6399162,8176707,
%U A113335 10328472,12910590,15984540,19617390,23882040,28857465,34628958,41288373,48934368,57672648,67616208
%N A113335 a(n) = 3^5 * binomial(n+4, 5).
%H A113335 G. C. Greubel, <a href="/A113335/b113335.txt">Table of n, a(n) for n = 1..1000</a>
%H A113335 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A113335 a(n) = 3^5 * binomial(n+4, 5), n >= 1.
%F A113335 From _G. C. Greubel_, May 17 2021: (Start)
%F A113335 G.f.: 243*x/(1-x)^6.
%F A113335 E.g.f.: (81/40)*x*(120 + 240*x + 120*x^2 + 20*x^3 + x^4)*exp(x). (End)
%F A113335 From _Amiram Eldar_, Aug 29 2022: (Start)
%F A113335 Sum_{n>=1} 1/a(n) = 5/972.
%F A113335 Sum_{n>=1} (-1)^(n+1)/a(n) = 80*log(2)/243 - 655/2916. (End)
%p A113335 seq(binomial(n+4,5)*3^5, n=1..27);
%t A113335 With[{c=3^5},Table[c Binomial[n+4,5],{n,30}]]  (* _Harvey P. Dale_, Apr 11 2011 *)
%o A113335 (Magma) [3^5*Binomial(n+4,5): n in [1..30]]; // _G. C. Greubel_, May 17 2021
%o A113335 (Sage) [3^5*binomial(n+4,5) for n in (1..30)] # _G. C. Greubel_, May 17 2021
%Y A113335 Cf. A027465.
%Y A113335 Sequences of the form 3^m*binomial(n+m-1, m): A008585 (m=1), A027468 (m=2), A134171 (m=3), A102741 (m=4), this sequence (m=5).
%K A113335 nonn,easy
%O A113335 1,1
%A A113335 _Zerinvary Lajos_, Aug 06 2008