cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A302189 Hurwitz inverse of squares [1,4,9,16,...].

This page as a plain text file.
%I A302189 #24 Apr 15 2018 17:04:15
%S A302189 1,-4,23,-184,1933,-25316,397699,-7288408,152650649,-3596802148,
%T A302189 94165506031,-2711813462744,85195437862693,-2899579176456964,
%U A302189 106276755720182363,-4173542380352243896,174823612884063939889,-7780800729631450594628
%N A302189 Hurwitz inverse of squares [1,4,9,16,...].
%C A302189 In the ring of Hurwitz sequences all members have offset 0.
%D A302189 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 A302189 Seiichi Manyama, <a href="/A302189/b302189.txt">Table of n, a(n) for n = 0..387</a>
%H A302189 N. J. A. Sloane, <a href="/A302189/a302189.txt">Maple programs for operations on Hurwitz sequences</a>
%F A302189 E.g.f. = 1 / Sum_{n >= 0} (n+1)^2*x^n/n!.
%F A302189 From _Vaclav Kotesovec_, Apr 15 2018: (Start)
%F A302189 E.g.f: exp(-x)/(1 + 3*x + x^2).
%F A302189 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 A302189 (End)
%p A302189 # first load Maple commands for Hurwitz operations from link
%p A302189 s:=[seq(n^2,n=1..64)];
%p A302189 Hinv(s);
%t A302189 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 A302189 Cf. A302870.
%K A302189 sign
%O A302189 0,2
%A A302189 _N. J. A. Sloane_ and William F. Keigher, Apr 12 2018