A355229 E.g.f. A(x) satisfies A'(x) = 1 - log(1-x) * A(x).

0, 1, 0, 2, 3, 16, 65, 365, 2261, 16240, 131097, 1182013, 11779537, 128737088, 1532051287, 19731964705, 273556185109, 4062828620256, 64368863326717, 1083795820014261, 19327395713028985, 363940825109825200, 7216468161637890899, 150304143164083288441

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Formula

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

E.g.f.: (1-x)^(1-x) / exp(1-x) * Integral(exp(1-x) / (1-x)^(1-x) dx). - Vaclav Kotesovec, Jun 25 2022

Mathematica

nmax = 25; CoefficientList[Series[(1-x)^(1-x) / E^(1-x) * Integrate[E^(1-x) / (1-x)^(1-x), x], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 25 2022 *)

Prog

(PARI) a_vector(n) = my(v=vector(n)); v[1]=1; for(i=1, n-1, v[i+1]=sum(j=1, i-1, (j-1)!*binomial(i, j)*v[i-j])); concat(0, v);

Crossrefs

Cf. A055596, A087650, A355230, A355231.

Sequence in context: A012705 A103331 A052506 * A052858 A191416 A209004

Adjacent sequences: A355226 A355227 A355228 * A355230 A355231 A355232

Keyword

nonn

Author

Seiichi Manyama, Jun 25 2022

Status

approved