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 A305407 Expansion of e.g.f. 1/(1 + log(1 - x)*exp(x)). 0
 1, 1, 5, 32, 274, 2939, 37833, 568210, 9753280, 188342949, 4041170695, 95380234366, 2455830637412, 68501591450447, 2057726452045145, 66227424015265178, 2273614433910697920, 82932491842062712873, 3202994529476330549163, 130577628147690206429038, 5603479009890212632226756 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) ~ n! / ((1 + exp(r)/r) * (1 - exp(-r))^(n+1)), where r = 0.62747017959751658496114808922921433658821962606026068561095... is the root of the equation r*exp(1 - exp(-r)) = 1. - Vaclav Kotesovec, Mar 26 2019 EXAMPLE E.g.f.: A(x) = 1 + x + 5*x^2/2! + 32*x^3/3! + 274*x^4/4! + 2939*x^5/5! + 37833*x^6/6! + ... MAPLE a:=series(1/(1+log(1-x)*exp(x)), x=0, 21): seq(n!*coeff(a, x, n), n=0..20); # Paolo P. Lava, Mar 26 2019 MATHEMATICA nmax = 20; CoefficientList[Series[1/(1 + Log[1 - x] Exp[x]), {x, 0, nmax}], x] Range[0, nmax]! a[0] = 1; a[n_] := a[n] = Sum[HypergeometricPFQ[{1, 1, 1 - k}, {2}, -1] a[n - k]/(k - 1)!, {k, 1, n}]; Table[n! a[n], {n, 0, 20}] CROSSREFS Cf. A002104, A006153, A007840, A009324. Sequence in context: A166993 A328055 A265130 * A320349 A001923 A257710 Adjacent sequences:  A305404 A305405 A305406 * A305408 A305409 A305410 KEYWORD nonn AUTHOR Ilya Gutkovskiy, May 31 2018 STATUS approved

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Last modified January 17 23:37 EST 2020. Contains 330995 sequences. (Running on oeis4.)