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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
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), 2163-2185, DOI: 10.1080/00927872.2016.1226885
LINKS
FORMULA
E.g.f. = 1 / Sum_{n >= 0} ((n+1)*(n+2)/2)*x^n/n!.
From Vaclav Kotesovec, Apr 26 2018: (Start)
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
Sequence in context: A235129 A222033 A341769 * A359660 A196559 A111262
KEYWORD
sign
AUTHOR
N. J. A. Sloane and William F. Keigher, Apr 14 2018
STATUS
approved