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Search: id:A157675
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| A157675 |
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G.f.: A(x) = exp( Sum_{n>=1} A(2^n*x)^n * x^n/n ). |
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4
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| 1, 1, 3, 19, 237, 5741, 270857, 25099497, 4605241487, 1681614043919, 1225216121453227, 1783355695990213771, 5188617952349909215215, 30183911091753947571225583, 351131331387346570480797774119
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Conjectured to consist entirely of integers.
Compare to: C(x) = exp( Sum_{n>=1} C(x)^n*x^n/n ) where C(x) = g.f. of Catalan numbers (A000108).
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EXAMPLE
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G.f.: A(x) = 1 + x + 3*x^2 + 19*x^3 + 237*x^4 + 5741*x^5 + 270857*x^6 +...
A(x) = exp(A(2x)*x + A(4x)^2*x^2/2 + A(8x)^3*x^3/3 + A(16x)^4*x^4/4 +...).
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PROGRAM
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, subst(A, x, 2^m*x +x*O(x^n))^m*x^m/m))); polcoeff(A, n)}
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CROSSREFS
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Cf. A156907.
Sequence in context: A003111 A126444 A001929 this_sequence A135754 A118023 A054590
Adjacent sequences: A157672 A157673 A157674 this_sequence A157676 A157677 A157678
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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), Mar 06 2009
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