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A049299
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a(n) = Product_{k = 0..n-1} (a(k) + a(n-1-k)), with a(0) = 1.
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1
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OFFSET
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0,2
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 0..8
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FORMULA
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lim_{m -> oo} log(a(m+1))/log(a(m)) exists and equals 3. - Roland Bacher, Sep 06 2004.
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EXAMPLE
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a(3)=400 because 400=(1+9)*(2+2)*(9+1).
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PROG
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(PARI) a(n)={my(v=vector(n+1)); for(n=1, #v, v[n]=prod(k=1, n-1, v[k]+v[n-k])); v[#v]} \\ Andrew Howroyd, Jan 02 2020
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CROSSREFS
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Cf. A000108 (Catalan numbers) where a(0) = 1, a(n) = Sum_{k=0..n-1} a(k)*a(n-k), A000012 (constant 1) where a(0) = 1, a(n) = Product_{k=0..n-1} a(k)*a(n-k) and A025192 (2*3^(n-1)) where a(0) = 1, a(n) = Sum_{k=0..n-1} a(k)+a(n-k). - Henry Bottomley, May 16 2000
Sequence in context: A012991 A003818 A325619 * A024225 A266289 A000883
Adjacent sequences: A049296 A049297 A049298 * A049300 A049301 A049302
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KEYWORD
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easy,nonn
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AUTHOR
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Leroy Quet
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EXTENSIONS
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Offset corrected and terms a(6) and beyond from Andrew Howroyd, Jan 02 2020
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STATUS
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approved
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