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Hurwitz logarithm of squares [1,4,9,16,...].
0

%I #17 Apr 11 2020 15:29:02

%S 0,4,-7,36,-282,2952,-38640,606960,-11123280,232968960,-5489285760,

%T 143711366400,-4138653657600,130021631308800,-4425213650457600,

%U 162195036421017600,-6369481772349696000,266808316331741184000,-11874725090839683072000

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

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

%H Xing Gao and William F. Keigher, <a href="https://doi.org/10.1080/00927872.2016.1226885">Interlacing of Hurwitz series</a>, Communications in Algebra, 45:5 (2017), 2163-2185, DOI: 10.1080/00927872.2016.1226885.

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

%p # first load Maple commands for Hurwitz operations from link in A302189.

%p s:=[seq(n^2,n=1..30)];

%p Hlog(s);

%o (Sage)

%o A = PowerSeriesRing(QQ, 'x')

%o f = A([i**2 for i in range(1,30)]).ogf_to_egf().log()

%o print(list(f.egf_to_ogf()))

%o # _F. Chapoton_, Apr 11 2020

%Y Cf. A302189.

%K sign

%O 0,2

%A _N. J. A. Sloane_ and William F. Keigher, Apr 14 2018