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A159597
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G.f.: A(x) = exp( Sum_{n>=1} [ D^n x/(1-x)^3 ]^n/n ), where differential operator D = x*d/dx.
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2
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1, 1, 7, 37, 245, 2094, 24661, 410376, 9809637, 334520167, 16192227784, 1107914634442, 106788033119369, 14525652771018918, 2780328926392863928, 751651711717655433750, 286240041470280077141769
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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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G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k>=1} k^n*k(k+1)/2*x^k]^n/n ) where A(x) = Sum_{k>=1} a(k)*x^k.
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EXAMPLE
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G.f.: A(x) = 1 + x + 7*x^2 + 37*x^3 + 245*x^4 + 2094*x^5 +...
log(A(x)) = Sum_{n>=1} [x + 2^n*3*x^2 + 3^n*6*x^3 +...]^n/n.
D^n x/(1-x)^3 = x + 2^n*3*x^2 + 3^n*6*x^3 + 4^n*10*x^4 +...
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PROG
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(k=1, n, k^m*k*(k+1)/2*x^k+x*O(x^n))^m/m))); 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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