%I A121353
%S A121353 0,1,4,27,266,3431,54630,1034539,22705228,566596161,15841987280,
%T A121353 490535009519,16662348336366,616016353436023,24623991789104554,
%U A121353 1058215630578059799,48653295014801646200,2382953240094702604001
%N A121353 An A053984-like Bessel-Binet recursion found by Bob Hanlon's new survey 
               program: a[n] = (3*n - 2)*a[n - 1] - a[n - 2].
%C A121353 I had theorized that there were a related kind of Bessel-Binets of the 
               form: a[n]=(a0*n+c0)*a[n-1]+b0*a[n-2] Where the a0,b0 and c0 were 
               Integers. Bob Hanlon found ones with a0=2 in a program he wrote. 
               A053984 was already in OEIS. This one is a0=3
%F A121353 a(n) = (3*n-2)*a(n - 1) - a(n - 2) a(n)=(1/3) pi BesselJ[1/3 + n, 2/3] 
               BesselY[1/3, 2/3] - (1/3) pi BesselJ[1/3, 2/3] BesselY[1/3 + n, 2/
               3]
%t A121353 f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == (3*n - 2)*a[n - 1] 
               - a[n - 2], a[0] == 0, a[1] == 1}, a[n], n][[1]] // FullSimplify] 
               Rationalize[N[Table[f[n], {n, 0, 25}], 100], 0]
%Y A121353 Cf. A053984, A001503.
%Y A121353 Sequence in context: A000312 A050764 A052813 this_sequence A161633 A052871 
               A104653
%Y A121353 Adjacent sequences: A121350 A121351 A121352 this_sequence A121354 A121355 
               A121356
%K A121353 nonn,uned
%O A121353 1,3
%A A121353 Roger Bagula and Bob Hanlon (rlbagulatftn(AT)yahoo.com), Sep 05 2006