A355102 - OEIS

%I #9 Jun 19 2022 08:40:46

%S 1,2,8,36,112,-500,-10056,24220,2184480,-8762868,-1076904200,

%T 13388615108,954279034416,-32517111227484,-1095519424670888,

%U 104108720480963940,63376017498217152,-394143964914859213828,17135457626785509446184,1359360091138085321022956

%N E.g.f. A(x) satisfies A(x) = 1 + 2 * x * A(1 - exp(-x)).

%F a(0) = 1; a(n) = 2 * n * Sum_{k=0..n-1} (-1)^(n-k-1) * Stirling2(n-1,k) * a(k).

%F a(n) = 2 * n * A355093(n-1) for n>0.

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=2*i*sum(j=0, i-1, (-1)^(i-j-1)*stirling(i-1, j, 2)*v[j+1])); v;

%Y Cf. A354574, A355103.

%Y Cf. A355093.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jun 19 2022