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Search: id:A119821
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| A119821 |
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Coefficients of x^n in the n-th self-composition of x/(1-x)^2 for n>=1. |
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+0
4
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| 1, 4, 33, 436, 8015, 189596, 5494797, 188692708, 7494744807, 338103170428, 17079035749061, 955117390512858, 58584586487137113, 3910851585418994256, 282272352712037938081, 21904366942822876046020
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OFFSET
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1,2
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COMMENT
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The coefficient of x^n in the n-th self-composition of x/(1-x) = n^(n-1) = A000169(n); does this variant have a simple formula for a(n)?
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FORMULA
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a(n) = [x^n] F_n(x) where F_n(x) = F_{n-1}(F(x)) with F(x) = x/(1-x)^2.
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EXAMPLE
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The successive self-compositions of F(x) = x/(1-x)^2 begin:
F(x) = (1)x + 2x^2 + 3x^3 + 4x^4 + 5x^5 + 6x^6 + 7x^7 + 8x^8 +...
F(F(x)) = x + (4)x^2 + 14x^3 + 46x^4 + 145x^5 + 444x^6 + 1331x^7 +...
F(F(F(x))) = x + 6x^2 + (33)x^3 + 174x^4 + 892x^5 + 4480x^6 +...
F(F(F(F(x)))) = x + 8x^2 + 60x^3 + (436)x^4 + 3102x^5 + 21728x^6 +...
F(F(F(F(F(x))))) = x + 10x^2 + 95x^3 + 880x^4 + (8015)x^5 +72090x^6+..
F(F(F(F(F(F(x)))))) = x + 12x^2+138x^3+1554x^4+17255x^5+(189596)x^6+..
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PROGRAM
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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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Cf. A119820, A112317; A119819, A119817, A119815.
Sequence in context: A111534 A162655 A052885 this_sequence A102321 A002190 A101981
Adjacent sequences: A119818 A119819 A119820 this_sequence A119822 A119823 A119824
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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), Jun 01 2006
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