A355104 - OEIS

%I #9 Jun 19 2022 08:40:54

%S 1,2,8,36,128,-120,-5904,8792,1015808,-7346016,-403678560,9772765552,

%T 226781102016,-17673167204576,72041280334240,38308664521315920,

%U -1705420687695700992,-64315848872486436736,11313330167773175073408,-326450445457848188386944

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

%F a(0) = 1; a(n) = 2 * n * Sum_{k=0..n-1} Stirling1(n-1,k) * a(k).

%F a(n) = 2 * n * A355096(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, stirling(i-1, j, 1)*v[j+1])); v;

%Y Cf. A354729, A355105.

%Y Cf. A355096.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jun 19 2022