A302190 Hurwitz logarithm of natural numbers 1,2,3,4,5,...

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

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