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%I #23 Sep 08 2022 08:45:46
%S 0,144,1008,4032,12096,30240,66528,133056,247104,432432,720720,
%T 1153152,1782144,2673216,3907008,5581440,7814016,10744272,14536368,
%U 19381824,25502400,33153120,42625440,54250560,68402880,85503600,106024464,130491648,159489792,193666176
%N a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)/5.
%H Vincenzo Librandi, <a href="/A162669/b162669.txt">Table of n, a(n) for n = 0..1000</a>
%F From _R. J. Mathar_, Jul 13 2009: (Start)
%F a(n) = 144 * A000579(n+5).
%F G.f.: 144*x/(1-x)^7. (End)
%F E.g.f.: x*(720 +1800*x +1200*x^2 +300*x^3 +30*x^4 +x^5)*exp(x)/5. - _G. C. Greubel_, Aug 27 2019
%F From _Amiram Eldar_, Jan 09 2022: (Start)
%F Sum_{n>=1} 1/a(n) = 1/120.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/3 - 661/720. (End)
%p seq(144*binomial(n+5,6), n = 0..30); # _G. C. Greubel_, Aug 27 2019
%t CoefficientList[Series[144*x/(1-x)^7,{x,0,30}],x] (* _Vincenzo Librandi_, Mar 05 2012 *)
%t Table[(Times@@(n+Range[0,5]))/5,{n,0,30}] (* _Harvey P. Dale_, Jul 01 2019 *)
%t 144*Binomial[Range[30] +4, 6] (* _G. C. Greubel_, Aug 27 2019 *)
%o (Magma) [n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)/5: n in [1..30]]; // _Vincenzo Librandi_, Mar 05 2012
%o (PARI) vector(30, n, 144*binomial(n+4,6)) \\ _G. C. Greubel_, Aug 27 2019
%o (Sage) [144*binomial(n+5,6) for n in (0..30)] # _G. C. Greubel_, Aug 27 2019
%o (GAP) List([0..30], n-> 144*Binomial(n+5, 6)); # _G. C. Greubel_, Aug 27 2019
%Y Cf. A000579.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Jul 10 2009
%E Definition factorized, offset corrected by _R. J. Mathar_, Jul 13 2009
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