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%I #27 Sep 08 2022 08:45:08
%S 15,480,2145,5760,12075,21840,35805,54720,79335,110400,148665,194880,
%T 249795,314160,388725,474240,571455,681120,803985,940800,1092315,
%U 1259280,1442445,1642560,1860375,2096640,2352105,2627520,2923635,3241200,3580965,3943680
%N a(n) = (5*n+1)*(5*n+3)*(5*n+5).
%D R. Tijdeman, Some applications of Diophantine approximation, pp. 261-284 of Surveys in Number Theory (Urbana, May 21, 2000), ed. M. A. Bennett et al., Peters, 2003.
%H Vincenzo Librandi, <a href="/A079610/b079610.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F Sum_{n>=0} 1/a(n) is transcendental (cf. Tijdeman).
%F G.f.: 15*(1 + 28*x + 21*x^2)/(1-x)^4. - _Colin Barker_, Apr 28 2012
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Jun 23 2012
%t Times@@@(#+{1,3,5}&/@(5*Range[0,50])) (* _Harvey P. Dale_, Jan 01 2011 *)
%t LinearRecurrence[{4,-6,4, -1},{15,480,2145,5760},40] (* _Vincenzo Librandi_, Jun 23 2012 *)
%o (Magma) I:=[15, 480, 2145, 5760]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Jun 23 2012
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Jan 28 2003
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