

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
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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), 21632185, 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



