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%I #36 Jan 23 2025 08:30:43
%S -1,1,0,3,16,165,2016,30415,539904,11049129,256038400,6627314331,
%T 189517916160,5933803272397,201893195083776,7417376809230375,
%U 292648536838045696,12341039738944113105,553942486234823786496,26369048375194607316019,1326864458454400696320000
%N Expansion of e.g.f. -1/(1-LambertW(-x)).
%H G. C. Greubel, <a href="/A277458/b277458.txt">Table of n, a(n) for n = 0..385</a>
%H Jason Saied, Jeffrey Marshall, Namit Anand, and Eleanor G. Rieffel, <a href="https://arxiv.org/abs/2404.14217">General protocols for the efficient distillation of indistinguishable photons</a>, arxiv:2404.14217 [quant-ph], Apr 22 2024. See p. 14.
%F a(n) ~ n^(n-1) / 4.
%F a(n) = n!*Sum_{k = 1..n} (-1)^(k+1)*k*n^(n-k-1)/(n-k)! for n >= 1. Cf. A133297. - _Peter Bala_, Jul 23 2021
%F a(n) = (-1)^(n+1)*U(1-n, -n, -n) where U is the Kummer U function. - _Peter Luschny_, Jan 23 2025
%p seq(n!*add((-1)^(k+1)*k*n^(n-k-1)/(n-k)!, k = 1..n), n = 1..20); # _Peter Bala_, Jul 23 2021
%t CoefficientList[Series[-1/(1-LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
%o (PARI) my(x='x+O('x^50)); Vec(serlaplace(-1/(1 - lambertw(-x)))) \\ _G. C. Greubel_, Nov 07 2017
%Y Cf. A000312, A086331, A133297, A134095, A277510, A308506.
%K sign,easy,changed
%O 0,4
%A _Vaclav Kotesovec_, Oct 16 2016