A355229 -id:A355229

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A355230

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

+10
3

0, 1, 0, 4, 6, 144, 860, 30656, 497168, 33543808, 1300171872, 178516634624, 15640422963968, 4483114311886336, 862178272953520640, 520264199498699214848, 215806526739662643193856, 274505260166616222726586368

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..17.

FORMULA

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

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, 2^(i-j)*(j-1)!*binomial(i, j)*v[i-j])); concat(0, v);

CROSSREFS

Cf. A355086, A355229, A355231.

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jun 25 2022

STATUS

approved

A355231

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

+10
2

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

(list; graph; refs; listen; history; text; internal format)

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 *)