|
%I
%S 15,315,1287,3315,6783,12075,19575,29667,42735,59163,79335,103635,
%T 132447,166155,205143,249795,300495,357627,421575,492723,571455,
%U 658155,753207,856995,969903,1092315,1224615,1367187,1520415,1684683,1860375
%N a(n) = (4*n+1)*(4*n+3)*(4*n+5).
%D Jolley, Summation of Series, Dover (1961).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F G.f.: 3*(5 + 85*x + 39*x^2 - x^3)/(1-x)^4 .
%F E.g.f: (15 + 300*x + 336*x^2 + 64*x^3)*exp(x) .
%F sum(4/((4*m+1)*(4*m+3)*(4*m+5)), m=0..infinity) = (Pi-2)/4. [Jolley eq 238]
%F a(0)=15, a(1)=315, a(2)=1287, a(3)=3315; for n>3, a(n) = 4*a(n-1)-6*a(n-2)+ 4*a(n-3)- a(n-4). - _Harvey P. Dale_, May 06 2012
%p seq((4*n+1)*(4*n+3)*(4*n+5),n=0..40);
%t Table[c=4n;(c+1)(c+3)(c+5),{n,0,30}] (* or *) LinearRecurrence[{4,-6,4,-1},{15,315,1287,3315},30] (* _Harvey P. Dale_, May 06 2012 *)
%o (PARI) a(n)=(4*n+1)*(4*n+3)*(4*n+5) \\ _Charles R Greathouse IV_, Oct 16 2015
%K nonn,easy
%O 0,1
%A _Miklos Kristof_, Jan 02 2008
|
