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%I #27 Sep 20 2022 02:37:25
%S 1,126,1001,3876,10626,23751,46376,82251,135751,211876,316251,455126,
%T 635376,864501,1150626,1502501,1929501,2441626,3049501,3764376,
%U 4598126,5563251,6672876,7940751,9381251,11009376,12840751,14891626,17178876,19720001,22533126
%N a(n) = A001512(n)/24 = (5*n+1)*(5*n+2)*(5*n+3)*(5*n+4)/24.
%H Vincenzo Librandi, <a href="/A151989/b151989.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F Sum_{k>=0} 1/a(k) = 4*sqrt(10-22/sqrt(5))*Pi/5. - _Jaume Oliver Lafont_, May 22 2010
%F G.f.: (1 + 121*x + 381*x^2 + 121*x^3 + x^4)/(1-x)^5. - _Colin Barker_, Aug 17 2012
%F Sum_{n>=0} (-1)^n/a(n) = 32*log(2)/5 - 8*arccoth(3/sqrt(5))/sqrt(5). - _Amiram Eldar_, Sep 20 2022
%t (Times@@#)/24&/@Table[5n+i,{n,0,35},{i,4}] (* _Harvey P. Dale_, Aug 16 2011 *)
%t Table[Binomial[5*n+4,4], {n,0,30}] (* _G. C. Greubel_, Nov 08 2018 *)
%o (Magma) [(5*n+1)*(5*n+2)*(5*n+3)*(5*n+4)/24: n in [0..30]]; // _Vincenzo Librandi_, Aug 17 2011
%o (PARI) vector(30, n, n--; binomial(5*n+4,4)) \\ _G. C. Greubel_, Nov 08 2018
%Y Cf. A001512.
%K nonn,easy
%O 0,2
%A _M. F. Hasler_, Sep 14 2009
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