Search: id:a141361
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A141361
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E.g.f.: A(x) = exp(x*A(x) * exp(x*A(x)^2 * exp(x*A(x)^3 * exp(x*A(x)^4 * exp(...))))), an infinite power tower.
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4
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1, 1, 5, 55, 981, 24621, 803143, 32390247, 1560845289, 87688371385, 5637912173451, 408922311037659, 33077570245035517, 2956347175261764597, 289716070585295689455, 30931475430329804121871, 3578416722896540323224657, 446526125468639494991613297
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: A(x) = (1/x)*Series_Reversion(x/B(x)) where B(x) is the e.g.f. of A141360.
E.g.f.: A(x) = x/Series_Reversion(x*C(x)) where C(x) is the e.g.f. of A141362.
E.g.f.: A(x) = B(x*A(x)) 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)^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)^2) 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 + 5*x^2/2! + 55*x^3/3! + 981*x^4/4! + 24621*x^5/5! +...
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PROG
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(PARI) {a(n) = my(A=1+x + x*O(x^n), F); for(i=0, n+1, for(j=0, n, F = exp(x*(A + x*O(x^n))^(n-j+1) * F)); A=F); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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