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 A302189 Hurwitz inverse of squares [1,4,9,16,...]. 12
 1, -4, 23, -184, 1933, -25316, 397699, -7288408, 152650649, -3596802148, 94165506031, -2711813462744, 85195437862693, -2899579176456964, 106276755720182363, -4173542380352243896, 174823612884063939889, -7780800729631450594628 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In the ring of Hurwitz sequences all members have offset 0. REFERENCES Xing Gao and William F. Keigher, Interlacing of Hurwitz series, Communications in Algebra, 45:5 (2017), 2163-2185, DOI: 10.1080/00927872.2016.1226885 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..387 N. J. A. Sloane, Maple programs for operations on Hurwitz sequences FORMULA E.g.f. = 1 / Sum_{n >= 0} (n+1)^2*x^n/n!. From Vaclav Kotesovec, Apr 15 2018: (Start) E.g.f: exp(-x)/(1 + 3*x + x^2). 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. (End) MAPLE # first load Maple commands for Hurwitz operations from link s:=[seq(n^2, n=1..64)]; Hinv(s); MATHEMATICA nmax = 20; CoefficientList[Series[1/(E^x*(1 + 3*x + x^2)), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Apr 15 2018 *) CROSSREFS Cf. A302870. Sequence in context: A056814 A058863 A192840 * A292971 A317967 A186117 Adjacent sequences: A302186 A302187 A302188 * A302190 A302191 A302192 KEYWORD sign AUTHOR N. J. A. Sloane and William F. Keigher, Apr 12 2018 STATUS approved

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Last modified July 21 03:50 EDT 2024. Contains 374463 sequences. (Running on oeis4.)