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%I #54 Jul 17 2022 09:04:29
%S 1,-2,2,2,-6,-14,26,178,90,-2382,-9446,13746,287194,998578,-3687782,
%T -56264782,-208446118,1017677490,17194912282,79540574642,
%U -317691584294,-7577787031374,-47958156443238,77252406086578,4400217218583642,39757699729476274,54538870133137690
%N E.g.f.: exp(2*(1-exp(x))).
%C Exponential self-convolution of complementary Bell numbers (A000587). - _Vladimir Reshetnikov_, Oct 07 2016
%H Seiichi Manyama, <a href="/A213170/b213170.txt">Table of n, a(n) for n = 0..580</a>
%H Vaclav Kotesovec, <a href="/A213170/a213170.jpg">Graph - asymptotic (1000 terms)</a>
%F a(n) = Sum_{k=0..n} A048993(n,k)*(-2)^k.
%F a(n) = Sum_{k=0..n} A000587(k)*A000587(n-k)*binomial(n,k).
%F G.f.: 1/(1+2*x/(1-x/(1+2*x/(1-2*x/(1+2*x/(1-3*x/(1+2*x/(1-4*x/(1+2*x/(1-...(continued fraction).
%F Sum_{k=0..n} binomial(n,k)*a(k) = a(n+1)/(-2). - _Philippe Deléham_, Feb 17 2013
%F G.f.: 1/Q(0) where Q(k) = 1 + x*(k+1) + x/(1 - 2*x*(k+1)/Q(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Mar 07 2013
%F Lim sup n->infinity (abs(a(n))/n!)^(1/n) / abs(exp(1/LambertW(-n/2)) / LambertW(-n/2)) = 1. - _Vaclav Kotesovec_, Aug 04 2014
%F a(n) = B_n(-2), where B_n(x) is n-th Bell polynomial. - _Vladimir Reshetnikov_, Oct 20 2015
%F G.f.: Sum_{j>=0} (-2)^j*x^j / Product_{k=1..j} (1 - k*x). - _Ilya Gutkovskiy_, Apr 06 2019
%p b:= proc(n, m) option remember; `if`(n=0,
%p (-2)^m, m*b(n-1, m)+b(n-1, m+1))
%p end:
%p a:= n-> b(n, 0):
%p seq(a(n), n=0..27); # _Alois P. Heinz_, Jul 17 2022
%t CoefficientList[Series[E^(2*(1-E^x)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Aug 04 2014 *)
%t Table[BellB[n, -2], {n, 0, 20}] (* _Vladimir Reshetnikov_, Oct 20 2015 *)
%o (PARI) x='x+O('x^50); Vec(serlaplace(exp(2*(1-exp(x))))) \\ _G. C. Greubel_, Nov 15 2017
%Y Cf. A000587, A001861, A007318, A048993.
%K sign,easy
%O 0,2
%A _Philippe Deléham_, Feb 14 2013
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