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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 Seiichi Manyama, Table of n, a(n) for n = 0..400 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 Cf. A000217, A302189. Sequence in context: A235129 A222033 A341769 * A359660 A196559 A111262 Adjacent sequences: A302192 A302193 A302194 * A302196 A302197 A302198 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.)