A355231 E.g.f. A(x) satisfies A'(x) = 1 - 2 * log(1-x) * A(x).

0, 1, 0, 4, 6, 48, 200, 1364, 9016, 71088, 607920, 5772528, 59790720, 673839456, 8210152704, 107668087104, 1513106471040, 22700196933120, 362277092798208, 6130771723664640, 109694104262443008, 2069581743476587008, 41071931895114372096, 855436794313229319168

Offset

0,4

Links

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

Formula

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

E.g.f.: (1-x)^(2 - 2*x) / exp(2 - 2*x) * Integral(exp(2 - 2*x) / (1-x)^(2 - 2*x) dx). - Vaclav Kotesovec, Jun 25 2022

Mathematica

nmax = 25; CoefficientList[Series[(1-x)^(2 - 2*x)/E^(2 - 2*x) * Integrate[E^(2 - 2*x) / (1-x)^(2 - 2*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]=2*sum(j=1, i-1, (j-1)!*binomial(i, j)*v[i-j])); concat(0, v);

Crossrefs

Cf. A088500, A355205, A355229, A355230.

Sequence in context: A134592 A306705 A165658 * A066348 A330978 A183369

Adjacent sequences: A355228 A355229 A355230 * A355232 A355233 A355234

Keyword

nonn

Author

Seiichi Manyama, Jun 25 2022

Status

approved