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));
A377328
E.g.f. satisfies A(x) = 1 + A(x)^2 * (exp(x*A(x)^3) - 1).
Original entry on oeis.org
1, 1, 11, 250, 8789, 420646, 25536083, 1880370598, 162872596937, 16227667154806, 1828467483194975, 229904271890603014, 31913005486577248877, 4847412341607090455110, 799762918909215143560907, 142427688272456020835132518, 27231132645610171996487568017, 5563389652463220933157357670806
Offset: 0
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a(n) = sum(k=0, n, (3*n+2*k)!/(3*n+k+1)!*stirling(n, k, 2));
A377348
E.g.f. satisfies A(x) = 1 + (exp(x*A(x)^3) - 1)/A(x)^3.
Original entry on oeis.org
1, 1, 1, 10, 79, 946, 14653, 267478, 5817187, 145061146, 4089128425, 128703410254, 4470302200087, 169912192575490, 7014628977829237, 312570024564324358, 14952747796689292747, 764341021646724256426, 41578052013117358139809, 2398149800670737138081470
Offset: 0
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a(n) = sum(k=0, (3*n+1)\4, (3*n-3*k)!/(3*n-4*k+1)!*stirling(n, k, 2));
Showing 1-3 of 3 results.