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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..22.

Xing Gao and William F. Keigher, Interlacing of Hurwitz series, Communications in Algebra, 45:5 (2017), 2163-2185, DOI: 10.1080/00927872.2016.1226885. See Ex. 2.16.

N. J. A. Sloane, Maple programs for operations on Hurwitz sequences

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()))

# F. Chapoton, Apr 11 2020

CROSSREFS

Cf. A133942.

Sequence in context: A032163 A038078 A000139 * A114572 A052621 A212671

Adjacent sequences:  A302187 A302188 A302189 * A302191 A302192 A302193

KEYWORD

sign

AUTHOR

N. J. A. Sloane and William F. Keigher, Apr 12 2018

STATUS

approved

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Last modified October 17 11:10 EDT 2021. Contains 348048 sequences. (Running on oeis4.)