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A161971
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E.g.f. satisfies: A(x) = exp( x*exp( x*A'(x) ) ), where A'(x) = d/dx A(x).
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1
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1, 1, 3, 28, 521, 15596, 672457, 39049396, 2919995969, 272314100944, 30921124212881, 4195725816103724, 670156359448985521, 124435720115244671056, 26578720273153614206201
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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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a(n) ~ c * n * (n!)^2, where c = 0.2773256592699... - Vaclav Kotesovec, Aug 24 2017
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 3*x^2/2! + 28*x^3/3! + 521*x^4/4! + 15596*x^5/5! +...
exp(x*A'(x)) = 1 + x + 7*x^2/2! + 103*x^3/3! + 2565*x^4/4! + 94881*x^5/5! +...
where log(A(x)) = x*exp(x*A'(x)):
log(A(x)) = x + 2*x^2/2! + 21*x^3/3! + 412*x^4/4! + 12825*x^5/5! + 569286*x^6/6! +...
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PROG
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(x*exp(x*deriv(A)+O(x^n)))); n!*polcoeff(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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STATUS
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approved
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