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Search: id:A141360
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| A141360 |
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E.g.f.: A(x) = exp(x*exp(x*A(x)*exp(x*A(x)^2*exp(x*A(x)^3*exp(...))))), an infinite power tower. |
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+0
5
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| 1, 1, 3, 22, 281, 5276, 132577, 4209766, 162569969, 7430664952, 393986044961, 23861309117834, 1630730511310441, 124533452791281028, 10541716135649976929, 982527040998772635286, 100258434765654907227233
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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E.g.f.: A(x) = x/Series_Reversion(x*B(x)) where B(x) is the e.g.f. of A141361.
E.g.f.: A(x) = B(x/A(x)) where B(x) = exp(x*B(x)*exp(x*B(x)^2*exp(x*B(x)^3*exp(...)))) is the e.g.f. of A141361 = [1,1,5,55,981,24621,803143,32390247,...].
E.g.f.: A(x) = C(x/A(x)^2) where C(x) = exp(x*C(x)^2*exp(x*C(x)^3*exp(x*C(x)^4*exp(...)))) is the e.g.f. of A141362 = [1,1,7,106,2545,84516,3599869,187549426,...].
E.g.f.: A(x) = D(x/A(x)^3) where D(x) = exp(x*D(x)^3*exp(x*D(x)^4*exp(x*D(x)^5*exp(...)))) is the e.g.f. of A141363 = [1,1,9,175,5357,225461,12112675,792855043,...].
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 281*x^4/4! +
5276*x^5/5! +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x, F); for(i=0, n, for(j=0, n, F=exp(x*(A+x*O(x^n))^(n-j)*F)); A =F); n!*polcoeff(A, n)}
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CROSSREFS
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Cf. A141361, A141362, A141363; variant: A141356.
Adjacent sequences: A141357 A141358 A141359 this_sequence A141361 A141362 A141363
Sequence in context: A005264 A052892 A074706 this_sequence A135862 A122778 A108991
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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 28 2008
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