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 A308351 For n >= 2, a(n) = n*u(n-1) + n*(n-1)*u(n-2), where u = A292932; a(1)=1. 0
 1, 4, 18, 128, 1090, 11232, 134806, 1849696, 28550538, 489656720, 9237631150, 190115847792, 4238752713442, 101775333547552, 2618244556598310, 71846664091504064, 2094748778352174202, 64666725024407102064, 2107224874854168508126, 72279858915240296971600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS M. Couceiro, J. Devillet, All quasitrivial n-ary semigroups are reducible to semigroups, arXiv:1904.05968 [math.RA], 2019. FORMULA a(n) = n*A292932(n-1) + n*(n-1)*A292932(n-2) = A292933(n) + n*A292933(n-1) for n >= 2. E.g.f.: x*(1 + x)/(3 - 2*exp(x) + x). - Vaclav Kotesovec, Jun 05 2019 a(n) ~ n! * (r-2) / ((r-1) * (r-3)^n), where r = -LambertW(-1, -2*exp(-3)). - Vaclav Kotesovec, Jun 05 2019 MATHEMATICA nmax = 20; Rest[CoefficientList[Series[x*(1 + x)/(3 - 2*E^x + x), {x, 0, nmax}], x] * Range[0, nmax]!] (* Vaclav Kotesovec, Jun 05 2019 *) CROSSREFS Cf. A292932, A292933. Sequence in context: A073511 A108704 A001423 * A291335 A158341 A144272 Adjacent sequences:  A308348 A308349 A308350 * A308352 A308353 A308354 KEYWORD nonn,easy AUTHOR J. Devillet, May 21 2019 STATUS approved

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Last modified February 27 15:59 EST 2020. Contains 332307 sequences. (Running on oeis4.)