Search: id:A135075
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%I A135075
%S A135075 0,1,5,33,265,2505,27261,335757,4617461,70138689,1166295457,21072290241,
%T A135075 411069239997,8611025176533,192788027607293,4594027768539585,
%U A135075 116093660372707273,3101080076109154137,87305805274735566669
%N A135075 A binomial recursion : a(n)=q(n) (see comment).
%C A135075 Let z(1)=x and z(n)=1+sum(k=1,n-1,(1+binomial(n,k))*z(k)), then z(n)=p(n)*x+q(n). 
               Lim n-->infty p(n)/q(n)=(3*pi-14)/(8-3*pi)=3.2111824896280692148...
%D A135075 B. Cloitre, Binomial recursions, Pi and log2, in preparation 2007
%o A135075 (PARI) r=1;s=1;v=vector(120,j,x);for(n=2,120, g=r+sum(k=1,n-1,(s+binomial(n,
               k))*v[k]); v[n]=g); z(n)=v[n];p(n)=polcoeff(z(n),1);q(n)=polcoeff(z(n),
               0);a(n)=q(n);
%Y A135075 Cf. A135074.
%Y A135075 Sequence in context: A061253 A111530 A087633 this_sequence A049377 A129890 
               A120733
%Y A135075 Adjacent sequences: A135072 A135073 A135074 this_sequence A135076 A135077 
               A135078
%K A135075 nonn
%O A135075 1,3
%A A135075 Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 17 2007

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