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A144002
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E.g.f. A(x) satisfies: A(x) = 1 + Series_Reversion( Integral 1/A(x)^2 dx ).
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4
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1, 1, 2, 10, 88, 1152, 20448, 464608, 12998176, 435443328, 17106187520, 775347933312, 40025403691136, 2328514989726720, 151324140857050624, 10904257049278844416, 865717992565002800640, 75309304802558209263616, 7143418423952431605493760, 735668180680897524348745728
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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) satisfies: A'(x) = A(x*A(x))^2. - Paul D. Hanna, Nov 25 2014
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 2*x^2/2! + 10*x^3/3! + 88*x^4/4! + 1152*x^5/5! +...
Related expansions.
A(x*A(x)) = 1 + x + 4*x^2/2! + 28*x^3/3! + 320*x^4/4! + 5192*x^5/5! + 111120*x^6/6! + 2988528*x^7/7! + 97647136*x^8/8! + 3781129248*x^9 +...
A(x*A(x))^2 = 1 + 2*x + 10*x^2/2! + 80*x^3/3! + 960*x^4/4! + 15824*x^5/5! +...
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PROG
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+serreverse(intformal(1/A^2))); n!*polcoeff(A, n)}
for(n=0, 30, 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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STATUS
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approved
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