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%I #24 Apr 15 2018 17:04:15
%S 1,-4,23,-184,1933,-25316,397699,-7288408,152650649,-3596802148,
%T 94165506031,-2711813462744,85195437862693,-2899579176456964,
%U 106276755720182363,-4173542380352243896,174823612884063939889,-7780800729631450594628
%N Hurwitz inverse of squares [1,4,9,16,...].
%C In the ring of Hurwitz sequences all members have offset 0.
%D Xing Gao and William F. Keigher, Interlacing of Hurwitz series, Communications in Algebra, 45:5 (2017), 2163-2185, DOI: 10.1080/00927872.2016.1226885
%H Seiichi Manyama, <a href="/A302189/b302189.txt">Table of n, a(n) for n = 0..387</a>
%H N. J. A. Sloane, <a href="/A302189/a302189.txt">Maple programs for operations on Hurwitz sequences</a>
%F E.g.f. = 1 / Sum_{n >= 0} (n+1)^2*x^n/n!.
%F From _Vaclav Kotesovec_, Apr 15 2018: (Start)
%F E.g.f: exp(-x)/(1 + 3*x + x^2).
%F a(n) ~ (-1)^n * n! * exp(1/phi^2) * phi^(2*n + 2) / sqrt(5), where phi = A001622 = (1 + sqrt(5))/2 is the golden ratio.
%F (End)
%p # first load Maple commands for Hurwitz operations from link
%p s:=[seq(n^2,n=1..64)];
%p Hinv(s);
%t nmax = 20; CoefficientList[Series[1/(E^x*(1 + 3*x + x^2)), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Apr 15 2018 *)
%Y Cf. A302870.
%K sign
%O 0,2
%A _N. J. A. Sloane_ and William F. Keigher, Apr 12 2018
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