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A357031
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E.g.f. satisfies log(A(x)) = (exp(x * A(x)) - 1)^2 / 2.
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2
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1, 0, 1, 3, 22, 195, 2131, 28623, 445789, 7982355, 161208976, 3626200743, 89942239861, 2438520508515, 71754865476841, 2277574224716703, 77570723071721938, 2821841221403098995, 109200125293424385271, 4479379126010806153143, 194148151869063307919725
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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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a(n) = Sum_{k=0..floor(n/2)} (2*k)! * (n+1)^(k-1) * Stirling2(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_] = Exp[(Exp[x*A[x]] - 1)^2/2] + 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)*stirling(n, 2*k, 2)/(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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