A355229
E.g.f. A(x) satisfies A'(x) = 1 - log(1-x) * A(x).
Original entry on oeis.org
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
-
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 *)
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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);
A355231
E.g.f. A(x) satisfies A'(x) = 1 - 2 * log(1-x) * A(x).
Original entry on oeis.org
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
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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 *)
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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);
A355235
E.g.f. A(x) satisfies A'(x) = 1 - log(1-x) * A(2*x)/2.
Original entry on oeis.org
0, 1, 0, 2, 3, 40, 230, 4664, 69160, 2692320, 92337072, 7377183360, 561596031744, 94107667481472, 15571512343805184, 5506994273113257984, 1955013641428681233408, 1459378050438033715961856, 1101502067162420292961916928
Offset: 0
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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-1)*(j-1)!*binomial(i, j)*v[i-j])); concat(0, v);
Showing 1-3 of 3 results.