A367828 E.g.f. A(x) satisfies A(x) = (1 - log(1 - x) * A(2*x)) / (1 - x).

1, 2, 13, 209, 7874, 687194, 138026428, 63273019396, 65547617642192, 151904702763916944, 780028188748068778464, 8799101018162158392857376, 216405047530763040469557821568, 11527355297347542160143184818391680, 1322291382391922104463259686181056293632

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

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

Prog

(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;

Crossrefs

Cf. A052820, A367829.

Cf. A355086, A367830, A367845.

Sequence in context: A193550 A367830 A102585 * A227746 A078702 A259795

Adjacent sequences: A367825 A367826 A367827 * A367829 A367830 A367831

Keyword

nonn

Author

Seiichi Manyama, Dec 02 2023

Status

approved