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%I #20 Apr 26 2018 04:30:18
%S 1,-3,12,-64,441,-3771,38638,-461742,6306009,-96885451,1653938616,
%T -31057949748,636230845297,-14119481897379,337448486204586,
%U -8640908986912786,236015269236658833,-6849355531826261427,210466462952536609924
%N Hurwitz inverse of triangular numbers [1,3,6,10,15,...].
%C In the ring of Hurwitz sequences all members have offset 0.
%D Xing Gao and William F. Keigher, Interlacing of Hurwitz series, Communications in Algebra, 45:5 (2017), 2163-2185, DOI: 10.1080/00927872.2016.1226885
%H Seiichi Manyama, <a href="/A302195/b302195.txt">Table of n, a(n) for n = 0..400</a>
%F E.g.f. = 1 / Sum_{n >= 0} ((n+1)*(n+2)/2)*x^n/n!.
%F From _Vaclav Kotesovec_, Apr 26 2018: (Start)
%F E.g.f: exp(-x) / (1 + 2*x + x^2/2).
%F a(n) ~ (-1)^n * n! * exp(2 - sqrt(2)) * (1 + 1/sqrt(2))^(n+1) / sqrt(2).
%F (End)
%p # first load Maple commands for Hurwitz operations from link in A302189.
%p s:=[seq(n*(n+1)/2,n=1..64)];
%p Hinv(s);
%t nmax = 20; CoefficientList[Series[1/(E^x*(1 + 2*x + x^2/2)), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Apr 26 2018 *)
%Y Cf. A000217, A302189.
%K sign
%O 0,2
%A _N. J. A. Sloane_ and William F. Keigher, Apr 14 2018
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