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%I #9 Jul 01 2020 20:23:56
%S 1,0,3,29,397,6879,144751,3587100,102351929,3305310065,119186370091,
%T 4746969337923,206966647324933,9804683604806908,501491905963040903,
%U 27544070654283355889,1616869985889305862385,101020181695996141703335,6693303018177050431484035,468770856837303230888704208
%N a(n) = exp(-n) * Sum_{k>=0} n^k * (k - 1)^n / k!.
%H Seiichi Manyama, <a href="/A335867/b335867.txt">Table of n, a(n) for n = 0..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>
%F a(n) = n! * [x^n] exp(n*(exp(x) - 1) - x).
%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * BellPolynomial_k(n).
%t Table[n! SeriesCoefficient[Exp[n (Exp[x] - 1) - x], {x, 0, n}], {n, 0, 19}]
%t Table[Sum[(-1)^(n - k) Binomial[n, k] BellB[k, n], {k, 0, n}], {n, 0, 19}]
%Y Cf. A000296, A217924, A242817, A334240, A335868.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jun 27 2020
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