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A335868 a(n) = exp(n) * Sum_{k>=0} (-n)^k * (k - 1)^n / k!. 5

%I

%S 1,-2,7,-31,149,-631,475,43210,-844727,10960505,-86569889,-584746911,

%T 46302579229,-1304510879686,25366896568707,-277053418780891,

%U -4271166460501743,384590020131637825,-14617527176248527545,380117694164438489422,-5265650620303861935579

%N a(n) = exp(n) * Sum_{k>=0} (-n)^k * (k - 1)^n / k!.

%H Seiichi Manyama, <a href="/A335868/b335868.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*(1 - exp(x)) - x).

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * BellPolynomial_k(-n).

%t Table[n! SeriesCoefficient[Exp[n (1 - Exp[x]) - x], {x, 0, n}], {n, 0, 20}]

%t Table[Sum[(-1)^(n - k) Binomial[n, k] BellB[k, -n], {k, 0, n}], {n, 0, 20}]

%Y Cf. A109747, A292866, A334241, A335867.

%K sign

%O 0,2

%A _Ilya Gutkovskiy_, Jun 27 2020

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Last modified June 19 23:27 EDT 2021. Contains 345154 sequences. (Running on oeis4.)