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Search: id:A153852
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| A153852 |
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Nonzero coefficients of g.f.: A(x) = G(G(x)) where G(x) = x + G(G(x))^3 is the g.f. of A153851. |
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+0
5
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| 1, 2, 15, 165, 2213, 33693, 561867, 10053141, 190489374, 3788856192, 78613758564, 1693737431667, 37760673462507, 868775517322730, 20583609967109565, 501340716386677815, 12535093359045980151, 321360932709750239226
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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G.f.: A(x) = Sum_{n>=0} a(2n+1)*x^(2n+1) = G(G(x)) where G(x) is the g.f. of A153851.
G.f.: A(x) = G(x) + x^2*H(x)^3 where G(x) is the g.f. of A153851 and H(x) is the g.f. of A153853.
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EXAMPLE
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G.f.: A(x) = x + 2*x^3 + 15*x^5 + 165*x^7 + 2213*x^9 +...
A(x)^3 = x^3 + 6*x^5 + 57*x^7 + 683*x^9 + 9474*x^11 + 145815*x^13 +...
A(x) = G(G(x)) where
G(x) = x + x^3 + 6*x^5 + 57*x^7 + 683*x^9 + 9474*x^11 +...
Let H(x) = g.f. of A153853, then A(x) = G(x) + x^2*H(x)^3 where
H(x) = x + 3*x^3 + 27*x^5 + 339*x^7 + 5067*x^9 + 84738*x^11 +...
H(x)^3 = x^3 + 9*x^5 + 108*x^7 + 1530*x^9 + 24219*x^11 +...
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PROGRAM
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(PARI) {a(n)=local(G=x+O(x^(2*n+1))); for(i=0, n, G=serreverse(x-G^3)); polcoeff(subst(G, x, G), 2*n-1)}
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CROSSREFS
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Cf. A153851, A153853, A153854, A153850.
Sequence in context: A124548 A139085 A140809 this_sequence A117667 A036080 A121427
Adjacent sequences: A153849 A153850 A153851 this_sequence A153853 A153854 A153855
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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 21 2009
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