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Search: id:A112319
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| A112319 |
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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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+0
4
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| 1, 1, 2, 9, 64, 630, 7916, 121023, 2179556, 45179508, 1059312264, 27715541568, 800423573676, 25289923553700, 867723362137464, 32128443862364255, 1276818947065793736, 54208515369076658640, 2448636361058495090816
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OFFSET
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1,3
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FORMULA
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a(n) = [x^n] F_{n-1}(x) where F_n(x) = F_{n-1}(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 + (1)*x^2
F(F(x)) = x + 2*x^2 + (2)*x^3 + x^4
F(F(F(x))) = x + 3*x^2 + 6*x^3+ (9)*x^4 +...
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 + (630)*x^6 +...
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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, G=subst(F, x, G)); return(polcoeff(G, n, x)))}
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CROSSREFS
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Cf. A112317, A112320.
Sequence in context: A000169 A055860 A152917 this_sequence A038038 A048801 A152915
Adjacent sequences: A112316 A112317 A112318 this_sequence A112320 A112321 A112322
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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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