A377324
E.g.f. satisfies A(x) = 1 + (exp(x*A(x)^3) - 1)/A(x).
Original entry on oeis.org
1, 1, 5, 52, 839, 18436, 513797, 17366224, 690366875, 31565619916, 1632064968929, 94159057903384, 5996889060457055, 417920884113926740, 31634205840603000221, 2584579552124805784672, 226699825143636127509347, 21247444370267806167804316, 2119206766514801966851437113
Offset: 0
-
a(n) = sum(k=0, n, (3*n-k)!/(3*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
-
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
-
a(n) = sum(k=0, (3*n+1)\4, (3*n-3*k)!/(3*n-4*k+1)!*stirling(n, k, 2));
A385059
E.g.f. A(x) satisfies A(x) = exp(x*A(x)/A(-x*A(x))^2).
Original entry on oeis.org
1, 1, 7, 40, 397, 2336, -46601, -2661896, -125428775, -3724273664, -90080842229, 1096530753176, 400257318802213, 36023363702572000, 2951479723885410943, 178834401869241704056, 8444450128124255913649, -59239960097902788177664, -92000068200778017857238125
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-n+k)^(j-1)*binomial(n, j)*a(n-j, 2*j)));
A385085
a(n) = 2 * (3*n+2)^(n-1).
Original entry on oeis.org
1, 2, 16, 242, 5488, 167042, 6400000, 296071778, 16063620352, 1000492825922, 70368744177664, 5517094707031250, 477144100447105024, 45126980600732372162, 4633559988356427808768, 513333972375334818668738, 61035156250000000000000000, 7752538100237033690795744642
Offset: 0