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A307724
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G.f. A(x) satisfies: A(x) = x*exp(Sum_{n>=1} Sum_{k>=1} n^k*a(n)^k*x^(n*k)/k).
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1
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0, 1, 1, 3, 12, 64, 402, 2999, 25100, 236278, 2444779, 27725926, 340761474, 4522224643, 64378645709, 979609661544, 15862570817855, 272466359964053, 4948142926019039, 94748748685737418, 1907956061833749740, 40310880538563569017, 891655630401500129652, 20608302703021633063682
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * Product_{n>=1} 1/(1 - n*a(n)*x^n).
Recurrence: a(n+1) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d*(d*a(d))^(k/d) ) * a(n-k+1).
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EXAMPLE
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G.f.: A(x) = x + x^2 + 3*x^3 + 12*x^4 + 64*x^5 + 402*x^6 + 2999*x^7 + 25100*x^8 + 236278*x^9 + ...
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MATHEMATICA
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a[n_] := a[n] = SeriesCoefficient[x Exp[Sum[Sum[j^k a[j]^k x^(j k)/k, {k, 1, n - 1}], {j, 1, n - 1}]], {x, 0, n}]; a[1] = 1; Table[a[n], {n, 0, 23}]
a[n_] := a[n] = SeriesCoefficient[x Product[1/(1 - k a[k] x^k), {k, 1, n - 1}], {x, 0, n}]; a[1] = 1; Table[a[n], {n, 0, 23}]
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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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