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A159316
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E.g.f. A(x) satisfies: d/dx log(A(x)) = A(2*x)^2.
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2
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1, 1, 5, 61, 1481, 66361, 5390285, 803252341, 224927827601, 121129543555441, 127545238071714965, 265238370995975176621, 1095520296374502654008921, 9015241470782090221556516521, 148067303294213271502974778276445
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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E.g.f. satisfies: A'(x) = A(x)*A(2*x)^2.
a(n) = Sum_{i=0..n-1} C(n-1,i)*4^i*A126444(i)*a(n-1-i) for n>0 with a(0)=1.
E.g.f.: A(x) = G(2*x)^(1/2) where G(x) = e.g.f. of A126444.
E.g.f.: A(x) = F(4*x)^(1/4) where F(x) = e.g.f. of A159315.
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EXAMPLE
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E.g.f.: A(x) = 1 +x +5*x^2/2! +61*x^3/3!+1481*x^4/4!+66361*x^5/5! +...
Related expansions:
log(A(x)) = x + 4*x^2/2! + 48*x^3/3! + 1216*x^4/4! + 57600*x^5/5! +...
A(2*x)^2 = 1 + 4*x + 48*x^2/2! + 1216*x^3/3! + 57600*x^4/4! +...
A(x)*A(2*x)^2 = 1 + 5*x +61*x^2/2! +1481*x^3/3! +66361*x^4/4! +...
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PROG
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(PARI) {a(n)=local(A=vector(n+4, j, 1+j*x)); for(i=0, n+3, for(j=0, n+2, m=n+3-j; A[m]=exp(intformal((A[m+1]+x*O(x^n))^(2^(m-1)))))); n!*polcoeff(A[3], n, x)}
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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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