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A125279
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G.f.: A(x) = (1/x)*series_reversion(x^2/G(x)) where G(x) is the g.f. of A030266, which shifts left under self-COMPOSE.
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1
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1, 1, 3, 13, 68, 400, 2555, 17375, 124280, 927711, 7189102, 57627044, 476645965, 4061184195, 35604795538, 320957712849, 2973550524004, 28305757130713, 276806230525768, 2780528226936569, 28686373905833717, 303913110837114965
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Derived from central terms of triangle: a(n) = A125278(2*n,n)/(n+1).
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FORMULA
| G.f. satisfies: A(x) = 1 + x*A(x)^2 * A( x^2*A(x)^4/(A(x) - 1) ). By definition, G.f. satisfies: A(x) = 1 + G(x*A(x)^2); G(x*A(x)) = x*A(x)^2; x*A(x^2/G(x)) = G(x); where G(x) = x + x*G(G(x)) is g.f. of A030266.
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EXAMPLE
| A(x) = 1 + x + 3*x^2 + 13*x^3 + 68*x^4 + 400*x^5 + 2555*x^6 +...
The g.f. of A030266 is G(x) = x + x*G(G(x)) where
G(x) = x + x^2 + 2*x^3 + 6*x^4 + 23*x^5 + 104*x^6 + 531*x^7 + 2982*x^8+..
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PROG
| (PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+x*A^2*subst(A, x, x^2*A^4/(A-1+x^2*O(x^n)))); polcoeff(A, n, x)}
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CROSSREFS
| Cf. A030266, A125278.
Sequence in context: A200757 A000260 A192737 * A186371 A121954 A058307
Adjacent sequences: A125276 A125277 A125278 * A125280 A125281 A125282
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Nov 26 2006
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