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Search: id:A112317
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| A112317 |
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Coefficients of x^n in the n-th self-composition of (x + x^2) for n>=1. |
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+0
12
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| 1, 2, 6, 30, 220, 2170, 27076, 409836, 7303164, 149837028, 3479498880, 90230486346, 2584679465160, 81056989408928, 2762187020749144, 101633218030586364, 4015771398425994048, 169588657820702174728
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = [x^n] F_n(x) where F_n(x) = F_{n-1}(x+x^2) with F_1(x) = x+x^2.
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EXAMPLE
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F(x) = (1)*x + x^2
F(F(x)) = x + (2)*x^2 +...
F(F(F(x))) = x + 3*x^2 + (6)*x^3 +...
F(F(F(F(x)))) = x + 4*x^2 + 12*x^3 + (30)*x^4 +...
F(F(F(F(F(x))))) = x + 5*x^2 + 20*x^3 + 70*x^4 + (220)*x^5 +...
F(F(F(F(F(F(x)))))) = x + 6*x^2 + 30*x^3 + 135*x^4 + 560*x^5 + (2170)*x^6 +...
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PROGRAM
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(PARI) {a(n)=local(F=x+x^2, G=x+x*O(x^n)); if(n<1, 0, for(i=1, n, G=subst(F, x, G)); return(polcoeff(G, n, x)))}
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CROSSREFS
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Sequence in context: A091456 A108204 A088160 this_sequence A089459 A027882 A106209
Adjacent sequences: A112314 A112315 A112316 this_sequence A112318 A112319 A112320
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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), Sep 03 2005
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