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Search: id:A162286
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| A162286 |
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G.f. satisfies: A(x) = exp( Sum_{n>=1} [Sum{d|n} A(n*x/d)^d/d]*x^n ). |
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+0
2
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| 1, 1, 3, 10, 43, 232, 1658, 16041, 214998, 4034263, 106718470, 3996978281, 212525227794, 16073873629022, 1731645876520667, 265992096914842633, 58303791955275494006, 18248056245233786876850, 8159322089091615235254206
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f. satisfies: A(x) = 1/Product{k>=1} (1 - x^k*A(k*x)). [From Paul D. Hanna (pauldhanna(AT)juno.com), Jul 01 2009]
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EXAMPLE
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G.f.: A(x) = 1 + x + 3*x^2 + 10*x^3 + 43*x^4 + 232*x^5 + 1658*x^6 +...
log(A(x)) = A(x)*x + [A(2x) + A(x)^2/2]*x^2 + [A(3x) + A(x)^3/3]*x^3 + [A(4x) + A(2x)^2/2 + A(x)^4/4]*x^4 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sumdiv(m, d, m*subst(A, x, m*x/d+x*O(x^n))^d/d)*x^m/m))); polcoeff(A, n)}
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1/prod(k=1, n, 1-x^k*subst(A, x, k*x+x*O(x^n)))); polcoeff(A, n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Jul 01 2009]
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CROSSREFS
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Sequence in context: A030971 A006932 A001040 this_sequence A032269 A041737 A026682
Adjacent sequences: A162283 A162284 A162285 this_sequence A162287 A162288 A162289
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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 29 2009
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