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Search: id:A126444
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| A126444 |
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a(n) = Sum_{k=0..n-1} C(n-1,k)*a(k)*a(n-1-k)*2^k for n>0, with a(0)=1. |
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+0
5
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| 1, 1, 3, 19, 225, 4801, 185523, 13298659, 1815718305, 481790947681, 251592291767043, 260427247041910099, 536497603929547755585, 2204489516030261302702561, 18090090482887693483393912563
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Generated by a generalization of a recurrence for the factorials.
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FORMULA
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a(n) = Sum_{k=0..n*(n-1)/2} A126470(n,k)*2^k.
Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Nov 22 2008: (Start)
E.g.f. satisfies: A'(x) = A(x)*A(2x) with A(0)=1;
the logarithmic derivative of e.g.f. A(x) equals A(2x). (End)
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PROGRAM
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(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(n-1, k)*a(k)*a(n-1-k)*2^k))
(PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal(A*subst(A, x, 2*x+x*O(x^n)))); n!*polcoeff(A, n, x)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Nov 22 2008]
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CROSSREFS
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Cf. A126470.
Sequence in context: A136652 A136504 A003111 this_sequence A001929 A157675 A135754
Adjacent sequences: A126441 A126442 A126443 this_sequence A126445 A126446 A126447
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 01 2007
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