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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
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
Sequence in context: A298899 A205388 A121446 * A340598 A258193 A283220
KEYWORD
sign
AUTHOR
N. J. A. Sloane and William F. Keigher, Apr 14 2018
STATUS
approved

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Last modified June 17 23:38 EDT 2024. Contains 373468 sequences. (Running on oeis4.)