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Search: id:A143923
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| A143923 |
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E.g.f. A(x) satisfies: A(x) = 1 + x*exp(Integral A(x)^3 dx). |
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+0
3
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| 1, 1, 2, 12, 88, 860, 10392, 149044, 2478752, 46875492, 993291880, 23311581524, 600207989808, 16820818373476, 509711184710840, 16606143020005620, 578830045479469120, 21493718211307208420, 847057099952645864712
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Compare definition of e.g.f. A(x) to the trivial statement:
if F(x) = 1/(1-x) then F(x) = 1 + x*exp(Integral F(x) dx).
Here Integral F(x) dx does not include the constant of integration.
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FORMULA
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E.g.f. derivative: A'(x) = [1 + x*A(x)^3]*(A(x) - 1)/x.
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EXAMPLE
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E.g.f. A(x) = 1 + x + 2*x^2/2! + 12*x^3/3! + 88*x^4/4! + 860*x^5/5! +...
A(x)^3 = 1 + 3*x + 12*x^2/2! + 78*x^3/3! + 696*x^4/4! + 7740*x^5/5! +...
Let L(x) = Integral A(x)^3 dx where A(x) = 1 + x*exp(L(x)), then
L(x) = x + 3*x^2/2! + 12*x^3/3! + 78*x^4/4! + 696*x^5/5! +...
exp(L(x)) = 1 + x + 4*x^2/2! + 22*x^3/3! + 172*x^4/4! + 1732*x^5/5! +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*exp(intformal(A^3))); n!*polcoeff(A, n)}
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CROSSREFS
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Cf. A143922, A143924.
Sequence in context: A097237 A055531 A059435 this_sequence A079858 A121357 A098926
Adjacent sequences: A143920 A143921 A143922 this_sequence A143924 A143925 A143926
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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 2008
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