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Search: id:A112320
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| A112320 |
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Coefficients of x^n in the (n+1)-th self-composition of (x + x^2) for n>=1. |
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3
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| 1, 3, 12, 70, 560, 5810, 74760, 1153740, 20817588, 430604724, 10052947476, 261595087182, 7509722346204, 235808741944100, 8040824716606176, 295914258931377276, 11690732617035570008, 493527339623630078552
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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+1}(x) where F_{n+1}(x) = F_n(x+x^2) with F_1(x) = x+x^2 and F_0(x)=x for n>=1.
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EXAMPLE
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Initial terms in self-compositions of (x+x^2) are:
F(x) = x + x^2
F(F(x)) = (1)*x + 2*x^2 + 2*x^3 + x^4
F(F(F(x))) = x + (3)*x^2 + 6*x^3 + 9*x^4 + 10*x^5 +...
F(F(F(F(x)))) = x + 4*x^2 + (12)*x^3 + 30*x^4 + 64*x^5 +...
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 +...
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MAPLE
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{a(n)=local(F=x+x^2, G=x+x*O(x^n)); if(n<1, 0, for(i=1, n+1, G=subst(F, x, G)); return(polcoeff(G, n, x)))}
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CROSSREFS
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Cf. A112317, A112319.
Sequence in context: A125862 A077460 A001205 this_sequence A103366 A020530 A052676
Adjacent sequences: A112317 A112318 A112319 this_sequence A112321 A112322 A112323
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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 06 2005
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