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Search: id:A141362
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| A141362 |
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E.g.f.: A(x) = exp(x*A(x)^2*exp(x*A(x)^3*exp(x*A(x)^4*exp(x*A(x)^5*exp(...))))), an infinite power tower. |
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+0
5
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| 1, 1, 7, 106, 2545, 84516, 3599869, 187549426, 11569862497, 825476139784, 66913201813141, 6077199111018366, 611543851953714673, 67563014389049920924, 8132697862579447135021, 1059750845948899631017906
(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) = (1/x)*Series_Reversion(x/C(x)) where C(x) is the e.g.f. of A141361.
E.g.f.: A(x) = x/Series_Reversion(x*D(x)) where D(x) is the e.g.f. of A141363.
E.g.f.: A(x) = B(x*A(x)^2) where B(x) = exp(x*exp(x*B(x)*exp(x*B(x)^2*exp(x*B(x)^3*exp(...))))) is the e.g.f. of A141360 = [1,1,3,22,281,5276,132577,4209766,...].
E.g.f.: A(x) = C(x*A(x)) where C(x) = exp(x*C(x)*exp(x*C(x)^2*exp(x*C(x)^3*exp(...)))) is the e.g.f. of A141361 = [1,1,5,55,981,24621,803143,32390247,...].
E.g.f.: A(x) = D(x/A(x)) 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 + 7*x^2/2! + 106*x^3/3! + 2545*x^4/4! +
84516*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+2)*F)) ; A=F); n!*polcoeff(A, n)}
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CROSSREFS
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Cf. A141360, A141361, A141363; variant: A141358.
Adjacent sequences: A141359 A141360 A141361 this_sequence A141363 A141364 A141365
Sequence in context: A049210 A002486 A141358 this_sequence A075021 A138963 A141932
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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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