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Search: id:A141363
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| A141363 |
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E.g.f.: A(x) = exp(x*A(x)^3*exp(x*A(x)^4*exp(x*A(x)^5*exp(x*A(x)^6*exp(...))))), an infinite power tower. |
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+0
5
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| 1, 1, 9, 175, 5357, 225461, 12112675, 792855043, 61249418585, 5456747990665, 550924441708031, 62176714054787135, 7758184127489208517, 1060631125759075562, 797, 157674821045525700085499
(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/D(x)) where D(x) is the e.g.f. of A141362.
E.g.f.: A(x) = B(x*A(x)^3) 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)^2) 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)^2*exp(x*D(x)^3*exp(x*D(x)^4*exp(...)))) is the e.g.f. of A141362 = [1,1,7,106,2545,84516,3599869,187549426,...].
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 9*x^2/2! + 175*x^3/3! + 5357*x^4/4! +
225461*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+3)*F)) ; A=F); n!*polcoeff(A, n)}
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CROSSREFS
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Cf. A141360, A141361, A141362; variant: A141359.
Sequence in context: A027956 A003280 A141359 this_sequence A003711 A009009 A034221
Adjacent sequences: A141360 A141361 A141362 this_sequence A141364 A141365 A141366
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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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