A367162
E.g.f. satisfies A(x) = 1 + A(x)^2 * (exp(x*A(x)) - 1).
Original entry on oeis.org
1, 1, 7, 94, 1917, 52806, 1837511, 77372590, 3826454617, 217450806550, 13964683107195, 1000222945246878, 79058281093939109, 6835704081028512886, 641830800234353986639, 65035909964873069979598, 7073810997780630959477937, 822049309574436641341233366
Offset: 0
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a(n) = sum(k=0, n, (n+2*k)!/(n+k+1)!*stirling(n, k, 2));
A377326
E.g.f. satisfies A(x) = 1 + (exp(x*A(x)) - 1)/A(x).
Original entry on oeis.org
1, 1, 1, 4, 15, 96, 665, 6028, 60907, 725560, 9591549, 142574004, 2323440119, 41519079616, 803667844993, 16797423268252, 376458083887875, 9014414549836296, 229564623594841637, 6197477089425914692, 176767174407208663759, 5312208220728020517136, 167760328500471584529321
Offset: 0
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terms=23; A[]=1; Do[A[x] = 1 + (Exp[x*A[x]] - 1)/A[x]+ O[x]^terms // Normal, terms]; CoefficientList[Series[A[x],{x,0,terms}],x]Range[0,terms-1]! (* Stefano Spezia, Aug 28 2025 *)
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a(n) = sum(k=0, (n+1)\2, (n-k)!/(n-2*k+1)!*stirling(n, k, 2));
A367201
E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1) * A(x)^3.
Original entry on oeis.org
1, 1, 10, 200, 6167, 258607, 13748744, 886397829, 67211684890, 5861684458896, 578088714806497, 63617223837958309, 7728596914020856162, 1027393177458209939977, 148344954037140113652010, 23119776330887635387231580, 3868359765874829925197165527
Offset: 0
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a(n) = sum(k=0, n, (n+3*k+1)^(k-1)*stirling(n, k, 2));
Showing 1-3 of 3 results.