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Search: id:A158888
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| A158888 |
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G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(2^n*x)^n. |
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1
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| 1, 1, 3, 21, 305, 8785, 497089, 55504321, 12305179649, 5437293562113, 4797448178045953, 8459278545576012801, 29821007074850747998209, 210213196038821563873677313, 2963378701144932768795387346945
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Compare g.f. to the g.f. C(x) of the Catalan numbers:
C(x) = Sum_{n>=0} x^n * C(x)^n.
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EXAMPLE
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G.f.: A(x) = 1 + x + 3*x^2 + 21*x^3 + 305*x^4 + 8785*x^5 +...
A(2x) = 1 + 2*x + 12*x^2 + 168*x^3 + 4880*x^4 + 281120*x^5 +...
A(4x)^2 = 1 + 8*x + 112*x^2 + 3072*x^3 + 169216*x^4 +...
A(8x)^3 = 1 + 24*x + 768*x^2 + 41984*x^3 + 4411392*x^4 +...
A(16x)^4 = 1 + 64*x + 4608*x^2 + 507904*x^3 + 102432768*x^4 +...
A(32x)^5 = 1 + 160*x + 25600*x^2 + 5734400*x^3 + 2233466880*x^4 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x); for(n=2, n, A=sum(k=0, n, x^k*subst(A, x, x*2^k+x*O(x^n))^k)); polcoeff(A, n)}
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CROSSREFS
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Cf. A000108.
Sequence in context: A126461 A000681 A055555 this_sequence A005329 A134528 A118410
Adjacent sequences: A158885 A158886 A158887 this_sequence A158889 A158890 A158891
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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), May 01 2009
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