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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 December 3 15:15 EST 2021. Contains 349463 sequences. (Running on oeis4.)