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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
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
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.)