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A302195
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Hurwitz inverse of triangular numbers [1,3,6,10,15,...].
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2
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1, -3, 12, -64, 441, -3771, 38638, -461742, 6306009, -96885451, 1653938616, -31057949748, 636230845297, -14119481897379, 337448486204586, -8640908986912786, 236015269236658833, -6849355531826261427, 210466462952536609924
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OFFSET
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0,2
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COMMENTS
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In the ring of Hurwitz sequences all members have offset 0.
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REFERENCES
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Xing Gao and William F. Keigher, Interlacing of Hurwitz series, Communications in Algebra, 45:5 (2017), 2163-2185, DOI: 10.1080/00927872.2016.1226885
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LINKS
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FORMULA
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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)
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MAPLE
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# first load Maple commands for Hurwitz operations from link in A302189.
s:=[seq(n*(n+1)/2, n=1..64)];
Hinv(s);
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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