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%I #25 Oct 18 2022 15:25:18
%S 15,693,3315,9177,19575,35805,59163,90945,132447,184965,249795,328233,
%T 421575,531117,658155,803985,969903,1157205,1367187,1601145,1860375,
%U 2146173,2459835,2802657,3175935,3580965,4019043,4491465,4999527,5544525,6127755,6750513
%N a(n) = (6*n+1)*(6*n+3)*(6*n+5).
%H T. D. Noe, <a href="/A001520/b001520.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 From _Jaume Oliver Lafont_, Oct 20 2009: (Start)
%F G.f.: 3*(1+x)*(5+206*x+5*x^2)/(1-x)^4.
%F Sum_{k>=0} 1/a(k) = log(3)/16. (End)
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n >= 4. - _Jinyuan Wang_, Mar 10 2020
%F Sum_{n>=0} (-1)^n/a(n) = Pi/48. - _Amiram Eldar_, Sep 22 2022
%p A001520:=n->(6*n+1)*(6*n+3)*(6*n+5); seq(A001520(n), n=0..50); # _Wesley Ivan Hurt_, Mar 10 2014
%t Table[(6n+1)(6n+3)(6n+5), {n, 0, 50}] (* _Wesley Ivan Hurt_, Mar 10 2014 *)
%o (PARI) a(n)=(6*n+1)*(6*n+3)*(6*n+5) \\ _Charles R Greathouse IV_, Oct 18 2022
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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