login
E.g.f. A(x) satisfies A(x) = (1 - log(1 - x) * A(2*x)) / (1 - x).
2

%I #13 Dec 02 2023 13:14:46

%S 1,2,13,209,7874,687194,138026428,63273019396,65547617642192,

%T 151904702763916944,780028188748068778464,8799101018162158392857376,

%U 216405047530763040469557821568,11527355297347542160143184818391680,1322291382391922104463259686181056293632

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

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

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

%Y Cf. A052820, A367829.

%Y Cf. A355086, A367830, A367845.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 02 2023