A352139
Expansion of e.g.f. 1/(exp(x) - log(1 - x)).
Original entry on oeis.org
1, -2, 6, -27, 161, -1205, 10799, -113043, 1351461, -18183781, 271784079, -4469044657, 80160267791, -1557710354083, 32597642189657, -730897865864471, 17480390183397209, -444198879957594857, 11951585821669838395, -339434402344422296117
Offset: 0
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m = 19; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - Log[1 - x]), {x, 0, m}], x] (* Amiram Eldar, Mar 06 2022 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)-log(1-x))))
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a(n) = if(n==0, 1, -sum(k=1, n, ((k-1)!+1)*binomial(n, k)*a(n-k)));
A352147
Expansion of e.g.f. 1/(exp(x) + log(1 + x)).
Original entry on oeis.org
1, -2, 8, -51, 437, -4685, 60299, -905583, 15543989, -300163717, 6440430159, -152007707357, 3913861488767, -109171084473763, 3279401359094041, -105546729767585411, 3623462164916028569, -132169615185372857001, 5104616345453966073403
Offset: 0
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m = 18; Range[0, m]! * CoefficientList[Series[1/(Exp[x] + Log[1 + x]), {x, 0, m}], x] (* Amiram Eldar, Mar 06 2022 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)+log(1+x))))
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a(n) = if(n==0, 1, sum(k=1, n, ((-1)^k*(k-1)!-1)*binomial(n, k)*a(n-k)));
A352138
Expansion of e.g.f. 1/(exp(x) - log(1 + x)).
Original entry on oeis.org
1, 0, -2, 1, 17, -17, -401, 817, 16197, -49861, -1123633, 5354787, 105696447, -682603651, -14697824519, 131535803133, 2457119246745, -28321054685609, -572811846560453, 8626026427105983, 146289547341006011, -2784279036040263575, -51756654994427512331
Offset: 0
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m = 22; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - Log[1 + x]), {x, 0, m}], x] (* Amiram Eldar, Mar 06 2022 *)
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my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)-log(1+x))))
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a(n) = if(n==0, 1, -sum(k=1, n, ((-1)^k*(k-1)!+1)*binomial(n, k)*a(n-k)));
A352270
Expansion of e.g.f. 1/(2 - exp(x) + log(1 - x)).
Original entry on oeis.org
1, 2, 10, 75, 751, 9405, 141361, 2478959, 49683047, 1120216645, 28064294201, 773391141325, 23250533411821, 757231705088131, 26558855360366239, 998051946325525971, 40006049065833007891, 1703833370634756077097, 76833773059665726636621
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)+log(1-x))))
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a(n) = if(n==0, 1, sum(k=1, n, ((k-1)!+1)*binomial(n, k)*a(n-k)));
Showing 1-4 of 4 results.