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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 17 00:51 EDT 2024. Contains 373432 sequences. (Running on oeis4.)