A371044
E.g.f. satisfies A(x) = 1 + x^3*exp(x*A(x)).
Original entry on oeis.org
1, 0, 0, 6, 24, 60, 120, 5250, 80976, 726264, 4839120, 86487390, 2283242280, 42585905076, 590667519624, 10115535833130, 286758920451360, 8128299117822960, 186279550983756576, 4123388294626654134, 118916807955913504440, 4102548791571529697580
Offset: 0
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nmax = 20; CoefficientList[Series[1 - LambertW[-E^x*x^4]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Mar 10 2024 *)
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a(n) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n-3*k+1, k)/((n-3*k+1)*(n-3*k)!));
A370984
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^2*exp(x)) ).
Original entry on oeis.org
1, 0, 2, 6, 84, 860, 14430, 257082, 5678456, 140241096, 3952791450, 123539438990, 4266378769092, 160943793753756, 6592371152535350, 291260465060881890, 13809548247503299440, 699362685890810753552, 37679514498664685654706
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^2*exp(x)))/x))
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a(n) = sum(k=0, n\2, k^(n-2*k)*(n+k)!/(k!*(n-2*k)!))/(n+1);
A371045
E.g.f. satisfies A(x) = 1 + x^3*A(x)*exp(x*A(x)).
Original entry on oeis.org
1, 0, 0, 6, 24, 60, 840, 15330, 161616, 1572984, 29031120, 636008670, 11426850600, 210095235636, 5137568918664, 139255673359530, 3574532174656800, 95923063388359920, 2974073508961556256, 98747639807081454774, 3287535337205171488440
Offset: 0
A371046
E.g.f. satisfies A(x) = 1 + x^3*A(x)^2*exp(x*A(x)).
Original entry on oeis.org
1, 0, 0, 6, 24, 60, 1560, 25410, 242256, 3508344, 85882320, 1724406750, 32784999720, 839182482996, 24162605028744, 659439484706730, 19415319297457440, 658935736181053680, 23245444335085544736, 835819877947421773494, 32462532011236141677240
Offset: 0
Showing 1-4 of 4 results.