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%I #18 Apr 11 2020 15:28:28
%S 0,2,-1,2,-6,24,-120,720,-5040,40320,-362880,3628800,-39916800,
%T 479001600,-6227020800,87178291200,-1307674368000,20922789888000,
%U -355687428096000,6402373705728000,-121645100408832000,2432902008176640000,-51090942171709440000
%N Hurwitz logarithm of natural numbers 1,2,3,4,5,...
%C In the ring of Hurwitz sequences all members have offset 0.
%H Xing Gao and William F. Keigher, <a href="https://doi.org/10.1080/00927872.2016.1226885">Interlacing of Hurwitz series</a>, Communications in Algebra, 45:5 (2017), 2163-2185, DOI: 10.1080/00927872.2016.1226885. See Ex. 2.16.
%H N. J. A. Sloane, <a href="/A302189/a302189.txt">Maple programs for operations on Hurwitz sequences</a>
%F E.g.f. is log of Sum_{n >= 0} (n+1)*x^n/n!.
%p # first load Maple commands for Hurwitz operations from link
%p s:=[seq(n,n=1..64)];
%p Hlog(s);
%o (Sage)
%o A = PowerSeriesRing(QQ, 'x')
%o f = A(list(range(1,30))).ogf_to_egf().log()
%o print(list(f.egf_to_ogf()))
%o # _F. Chapoton_, Apr 11 2020
%Y Cf. A133942.
%K sign
%O 0,2
%A _N. J. A. Sloane_ and William F. Keigher, Apr 12 2018
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