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A302196 Hurwitz logarithm of triangular numbers [1,3,6,10,15,...]. 0
0, 3, -3, 10, -51, 348, -2970, 30420, -363510, 4964400, -76272840, 1302058800, -24450287400, 500871016800, -11115524019600, 265655410020000, -6802532278542000, 185802383710944000, -5392136656290384000, 165689154918679392000, -5374132518684161232000, 183484361312817364800000 (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..21.

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)*(n+2)/2)*x^n/n!.

MAPLE

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

s:=[seq(n*(n+1)/2, n=1..64)];

Hlog(s);

PROG

(Sage)

A = PowerSeriesRing(QQ, 'x')

f = A([binomial(i+2, 2) for i in range(30)]).ogf_to_egf().log()

print(list(f.egf_to_ogf()))

#F. Chapoton, Apr 11 2020

CROSSREFS

Cf. A000217, A302189.

Sequence in context: A298899 A205388 A121446 * A340598 A258193 A283220

Adjacent sequences:  A302193 A302194 A302195 * A302197 A302198 A302199

KEYWORD

sign

AUTHOR

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

STATUS

approved

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Last modified October 21 05:28 EDT 2021. Contains 348141 sequences. (Running on oeis4.)