

A302190


Hurwitz logarithm of natural numbers 1,2,3,4,5,...


0



0, 2, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000, 51090942171709440000
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OFFSET

0,2


COMMENTS

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


LINKS

Xing Gao and William F. Keigher, Interlacing of Hurwitz series, Communications in Algebra, 45:5 (2017), 21632185, DOI: 10.1080/00927872.2016.1226885. See Ex. 2.16.


FORMULA

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


MAPLE

# first load Maple commands for Hurwitz operations from link
s:=[seq(n, n=1..64)];
Hlog(s);


PROG

(Sage)
A = PowerSeriesRing(QQ, 'x')
f = A(list(range(1, 30))).ogf_to_egf().log()
print(list(f.egf_to_ogf()))


CROSSREFS



KEYWORD

sign


AUTHOR



STATUS

approved



