A302198 Hurwitz logarithm of squares [1,4,9,16,...].

0, 4, -7, 36, -282, 2952, -38640, 606960, -11123280, 232968960, -5489285760, 143711366400, -4138653657600, 130021631308800, -4425213650457600, 162195036421017600, -6369481772349696000, 266808316331741184000, -11874725090839683072000

Offset

0,2

Comments

In the ring of Hurwitz sequences all members have offset 0.

Links

Table of n, a(n) for n=0..18.

Xing Gao and William F. Keigher, Interlacing of Hurwitz series, Communications in Algebra, 45:5 (2017), 2163-2185, DOI: 10.1080/00927872.2016.1226885.

Formula

E.g.f. is log of Sum_{n >= 0} (n+1)^2*x^n/n!.

Maple

# first load Maple commands for Hurwitz operations from link in A302189.
s:=[seq(n^2, n=1..30)];
Hlog(s);

Prog

(Sage)
A = PowerSeriesRing(QQ, 'x')
f = A([i**2 for i in range(1, 30)]).ogf_to_egf().log()
print(list(f.egf_to_ogf()))
# F. Chapoton, Apr 11 2020

Crossrefs

Cf. A302189.

Sequence in context: A209480 A209339 A212500 * A279830 A367775 A245305

Adjacent sequences: A302195 A302196 A302197 * A302199 A302200 A302201

Keyword

sign

Author

N. J. A. Sloane and William F. Keigher, Apr 14 2018

Status

approved