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%I #11 Dec 29 2023 10:58:11
%S 1,-3,37,-29,2761,-97,-268271,14759,2804929,-9435089,3731508001,
%T 1185970223,-264025807957621,44820288709817,4570382525453089,
%U -336032650312339,23787999916667875201,4316502548043120587,-4994567510209019657318207
%N a(n) = numerator of b(n), where sum{m>=0} b(m)*x^m/m! = x/(sum{m>=1} H(m) x^m/m!) = exp(-x)*x/(sum{m>=1} x^m (-1)^(m+1)/(m!*m)). (H(m) = sum{k=1 to m} 1/k.).
%F b(0)=1. b(n) = -sum{k=1 to n} binomial(n,k) H(k+1) b(n-k)/(k+1).
%e 1/(1 + x * 3/(2 * 2) + x^2 * 11/(6 * 6) + x^3 * 25/(12 * 24) +...) = 1 -x * 3/4 + x^2 * 37/72 -x^3 * 29/96 ...
%t b[0] = 1;b[n_] := b[n] = -Sum[Binomial[n, k] *HarmonicNumber[k + 1]*b[n - k]/(k + 1), {k, n}];Numerator[Array[b, 20, 0]] (* _Ray Chandler_, Feb 19 2007 *)
%Y Cf. A128062.
%K frac,sign
%O 0,2
%A _Leroy Quet_, Feb 13 2007
%E Extended by _Ray Chandler_, Feb 19 2007
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