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A119820
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Coefficients of x^n in the n-th iteration of x*(1+x)^2 for n>=1.
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7
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1, 4, 27, 300, 4790, 101010, 2660028, 84191772, 3115739358, 132074618544, 6311492388432, 335744715016854, 19678501474466211, 1260060524755139120, 87519840721085385096, 6553840567691077634748, 526360263009035464610574
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = [x^n] F_n(x) where F_n(x) = F_{n-1}(F_1(x)) with F_1(x) = x*(1+x)^2.
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EXAMPLE
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The successive iterations of F(x) = x*(1+x)^2 begin:
F(x) = (1)x + 2x^2 + x^3
F(F(x)) = x + (4)x^2 + 10x^3 + 18x^4 + 23x^5 + 22x^6 + 15x^7 + 6x^8 +...
F(F(F(x))) = x + 6x^2 + (27)x^3 + 102x^4 + 333x^5 + 960x^6 + 2472x^7 +...
F(F(F(F(x)))) = x + 8x^2 + 52x^3 + (300)x^4 + 1578x^5 + 7692x^6 +...
F(F(F(F(F(x))))) = x + 10x^2 + 85x^3 + 660x^4 + (4790)x^5 + 32920x^6+...
F(F(F(F(F(F(x)))))) = x + 12x^2 +126x^3 +1230x^4+11385x^5+(101010)x^6+...
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PROG
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(PARI) {a(n)=local(F=x*(1+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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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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