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Search: id:A135075
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| A135075 |
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A binomial recursion : a(n)=q(n) (see comment). |
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8
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| 0, 1, 5, 33, 265, 2505, 27261, 335757, 4617461, 70138689, 1166295457, 21072290241, 411069239997, 8611025176533, 192788027607293, 4594027768539585, 116093660372707273, 3101080076109154137, 87305805274735566669
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OFFSET
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1,3
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COMMENT
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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...
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REFERENCES
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B. Cloitre, Binomial recursions, Pi and log2, in preparation 2007
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PROGRAM
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(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);
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CROSSREFS
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Cf. A135074.
Sequence in context: A061253 A111530 A087633 this_sequence A049377 A129890 A120733
Adjacent sequences: A135072 A135073 A135074 this_sequence A135076 A135077 A135078
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 17 2007
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