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a(n) = 3^5 * binomial(n+4, 5).
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%I #15 Aug 29 2022 04:39:51

%S 243,1458,5103,13608,30618,61236,112266,192456,312741,486486,729729,

%T 1061424,1503684,2082024,2825604,3767472,4944807,6399162,8176707,

%U 10328472,12910590,15984540,19617390,23882040,28857465,34628958,41288373,48934368,57672648,67616208

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

%H G. C. Greubel, <a href="/A113335/b113335.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(n) = 3^5 * binomial(n+4, 5), n >= 1.

%F From _G. C. Greubel_, May 17 2021: (Start)

%F G.f.: 243*x/(1-x)^6.

%F E.g.f.: (81/40)*x*(120 + 240*x + 120*x^2 + 20*x^3 + x^4)*exp(x). (End)

%F From _Amiram Eldar_, Aug 29 2022: (Start)

%F Sum_{n>=1} 1/a(n) = 5/972.

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 80*log(2)/243 - 655/2916. (End)

%p seq(binomial(n+4,5)*3^5, n=1..27);

%t With[{c=3^5},Table[c Binomial[n+4,5],{n,30}]] (* _Harvey P. Dale_, Apr 11 2011 *)

%o (Magma) [3^5*Binomial(n+4,5): n in [1..30]]; // _G. C. Greubel_, May 17 2021

%o (Sage) [3^5*binomial(n+4,5) for n in (1..30)] # _G. C. Greubel_, May 17 2021

%Y Cf. A027465.

%Y 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 nonn,easy

%O 1,1

%A _Zerinvary Lajos_, Aug 06 2008