A355105 - OEIS

%I #8 Jun 19 2022 08:40:58

%S 1,3,18,135,1044,6210,-5994,-760347,-3009960,261689616,1960394400,

%T -220644396522,-1043258760828,366570209524896,-3109452797977470,

%U -972076070389224105,36160406771040130320,3274635904971823559880,-331428842765036684941320

%N E.g.f. A(x) satisfies A(x) = 1 + 3 * x * A(log(1+x)).

%F a(0) = 1; a(n) = 3 * n * Sum_{k=0..n-1} Stirling1(n-1,k) * a(k).

%F a(n) = 3 * n * A355097(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]=3*i*sum(j=0, i-1, stirling(i-1, j, 1)*v[j+1])); v;

%Y Cf. A354729, A355104.

%Y Cf. A355097.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jun 19 2022