A302196 Hurwitz logarithm of triangular numbers [1,3,6,10,15,...].

0, 3, -3, 10, -51, 348, -2970, 30420, -363510, 4964400, -76272840, 1302058800, -24450287400, 500871016800, -11115524019600, 265655410020000, -6802532278542000, 185802383710944000, -5392136656290384000, 165689154918679392000, -5374132518684161232000, 183484361312817364800000

Offset: 0

Author

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

Keywords

• sign

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), 2163-2185, DOI: 10.1080/00927872.2016.1226885.

Crossrefs

Cf. A000217, A302189.

Programs

Maple

# first load Maple commands for Hurwitz operations from link in A302189.
s:=[seq(n*(n+1)/2,n=1..64)];
Hlog(s);

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

Formula

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