A375721
Expansion of e.g.f. 1 / (1 + 3 * log(1 - x))^2.
Original entry on oeis.org
1, 6, 60, 822, 14238, 297684, 7286076, 204251328, 6450932448, 226613038608, 8763294140064, 369900822475728, 16922169163019088, 833991953707934496, 44050579327333028448, 2482381132145285334912, 148660444826262311114880, 9427874254540824544312320
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*log(1-x))^2))
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a(n) = sum(k=0, n, 3^k*(k+1)!*abs(stirling(n, k, 1)));
A375899
E.g.f. satisfies A(x) = 1 / (1 + log(1 - x * A(x)^(1/2)))^2.
Original entry on oeis.org
1, 2, 12, 124, 1846, 36128, 879252, 25637680, 872159952, 33933231696, 1486845891696, 72473120203680, 3890486148311040, 228103117063828992, 14504759878784601600, 994346460412330358016, 73107707092779695687040, 5738844073788385570644480
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(1+log(1-x)))/x)^2))
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a(n) = 2*sum(k=0, n, (n+k+1)!*abs(stirling(n, k, 1)))/(n+2)!;
A382830
a(n) = Sum_{k=0..n} binomial(n+k-1,k) * |Stirling1(n,k)| * k!.
Original entry on oeis.org
1, 1, 8, 102, 1804, 40890, 1131108, 36948240, 1391945616, 59411849040, 2833582748160, 149347596487056, 8620256620495584, 540775669746661440, 36636074309252234880, 2665704585421541790720, 207329122282259073044736, 17165075378189396045777280, 1507206260097615729874083840
Offset: 0
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Table[Sum[Binomial[n + k - 1, k] Abs[StirlingS1[n, k]] k!, {k, 0, n}], {n, 0, 18}]
Table[n! SeriesCoefficient[1/(1 + Log[1 - x])^n, {x, 0, n}], {n, 0, 18}]