cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A302196 #16 Apr 11 2020 15:29:58
%S A302196 0,3,-3,10,-51,348,-2970,30420,-363510,4964400,-76272840,1302058800,
%T A302196 -24450287400,500871016800,-11115524019600,265655410020000,
%U A302196 -6802532278542000,185802383710944000,-5392136656290384000,165689154918679392000,-5374132518684161232000,183484361312817364800000
%N A302196 Hurwitz logarithm of triangular numbers [1,3,6,10,15,...].
%C A302196 In the ring of Hurwitz sequences all members have offset 0.
%H A302196 Xing Gao and William F. Keigher, <a href="https://doi.org/10.1080/00927872.2016.1226885">Interlacing of Hurwitz series</a>, Communications in Algebra, 45:5 (2017), 2163-2185, DOI: 10.1080/00927872.2016.1226885.
%F A302196 E.g.f. is log of Sum_{n >= 0} ((n+1)*(n+2)/2)*x^n/n!.
%p A302196 # first load Maple commands for Hurwitz operations from link in A302189.
%p A302196 s:=[seq(n*(n+1)/2,n=1..64)];
%p A302196 Hlog(s);
%o A302196 (Sage)
%o A302196 A = PowerSeriesRing(QQ, 'x')
%o A302196 f = A([binomial(i+2,2) for i in range(30)]).ogf_to_egf().log()
%o A302196 print(list(f.egf_to_ogf()))
%o A302196 #_F. Chapoton_, Apr 11 2020
%Y A302196 Cf. A000217, A302189.
%K A302196 sign
%O A302196 0,2
%A A302196 _N. J. A. Sloane_ and William F. Keigher, Apr 14 2018