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A357036
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E.g.f. satisfies A(x) = (1 - x * A(x))^(log(1 - x * A(x)) / 2).
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3
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1, 0, 1, 3, 26, 230, 2794, 39564, 663606, 12712104, 275171106, 6632699040, 176309074644, 5123121177096, 161577261004860, 5497133655605760, 200683752698028924, 7825434930630743616, 324616635150708044796, 14273994548639305751040, 663205761925601097418488
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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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E.g.f. satisfies log(A(x)) = log(1 - x * A(x))^2 / 2.
a(n) = Sum_{k=0..floor(n/2)} (2*k)! * (n+1)^(k-1) * |Stirling1(n,2*k)|/(2^k * k!).
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MATHEMATICA
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m = 21; (* number of terms *)
A[_] = 0;
Do[A[x_] = (1 - x*A[x])^(Log[1 - x*A[x]]/2) + O[x]^m // Normal, {m}];
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PROG
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(PARI) a(n) = sum(k=0, n\2, (2*k)!*(n+1)^(k-1)*abs(stirling(n, 2*k, 1))/(2^k*k!));
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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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