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%I #21 Aug 28 2022 04:30:30
%S 81,405,1215,2835,5670,10206,17010,26730,40095,57915,81081,110565,
%T 147420,192780,247860,313956,392445,484785,592515,717255,860706,
%U 1024650,1210950,1421550,1658475,1923831,2219805,2548665,2912760,3314520,3756456,4241160,4771305,5349645
%N a(n) = 3^4 * binomial(n+3, 4).
%H G. C. Greubel, <a href="/A102741/b102741.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F G.f.: 81*x/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009
%F E.g.f.: (27/8)*x*(24 + 36*x + 12*x^2 + x^3)*exp(x). - _G. C. Greubel_, May 17 2021
%F From _Amiram Eldar_, Aug 28 2022: (Start)
%F Sum_{n>=1} 1/a(n) = 4/243.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 32*log(2)/81 - 64/243. (End)
%p seq(binomial(n+3,4)*3^4, n=1..27);
%t With[{c=3^4},Table[c Binomial[n+3,4],{n,40}]] (* _Harvey P. Dale_, Mar 12 2011 *)
%o (Magma) [3^4*Binomial(n+3,4): n in [1..30]]; // _G. C. Greubel_, May 17 2021
%o (Sage) [3^4*binomial(n+3,4) 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), this sequence (m=4), A113335 (m=5).
%K nonn,easy
%O 1,1
%A _Zerinvary Lajos_, Aug 06 2008
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