

A302195


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


2



1, 3, 12, 64, 441, 3771, 38638, 461742, 6306009, 96885451, 1653938616, 31057949748, 636230845297, 14119481897379, 337448486204586, 8640908986912786, 236015269236658833, 6849355531826261427, 210466462952536609924
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OFFSET

0,2


COMMENTS

In the ring of Hurwitz sequences all members have offset 0.


REFERENCES

Xing Gao and William F. Keigher, Interlacing of Hurwitz series, Communications in Algebra, 45:5 (2017), 21632185, DOI: 10.1080/00927872.2016.1226885


LINKS



FORMULA

E.g.f. = 1 / Sum_{n >= 0} ((n+1)*(n+2)/2)*x^n/n!.
E.g.f: exp(x) / (1 + 2*x + x^2/2).
a(n) ~ (1)^n * n! * exp(2  sqrt(2)) * (1 + 1/sqrt(2))^(n+1) / sqrt(2).
(End)


MAPLE

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


MATHEMATICA

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 *)


CROSSREFS



KEYWORD

sign


AUTHOR



STATUS

approved



