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%I #10 Aug 18 2015 00:19:14
%S 1,2,3,16,5,128,525,2048,11025,32768,10395,262144,2081079,2097152,
%T 19324305,67108864,21332025,2147483648,25264228275,17179869184,
%U 224009490705,137438953472,218578957597,2199023255552,699533769675
%N a(n) = denominator of r(n): r(n) is such that, for every positive integer n, the continued fraction (of rational terms) [r(1);r(2),...,r(n)] equals n(n+1)/2, the n-th triangular number.
%F For n >=4, r(n) = -(2n-1)*(2n-3)/(n(n-2) r(n-1)).
%e The 4th triangular number, 10, equals 1 +(1/2 +1/(-10/3 +16/21)).
%e The 5th triangular number, 15, equals 1 +(1/2 +1/(-10/3 +1/(21/16 -5/16))).
%p L2cfrac := proc(L,targ) local a,i; a := targ ; for i from 1 to nops(L) do a := 1/(a-op(i,L)) ; od: end: A128537 := proc(nmax) local b,n,bnxt; b := [1] ; for n from nops(b)+1 to nmax do bnxt := L2cfrac(b,n*(n+1)/2) ; b := [op(b),bnxt] ; od: [seq( denom(b[i]),i=1..nops(b))] ; end: A128537(26) ; # _R. J. Mathar_, Oct 09 2007
%Y Cf. A128536.
%K frac,nonn
%O 1,2
%A _Leroy Quet_, Mar 09 2007
%E More terms from _R. J. Mathar_, Oct 09 2007
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