A370928
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x^3)) ).
Original entry on oeis.org
1, 1, 4, 30, 360, 5880, 120960, 2996280, 86889600, 2889976320, 108501724800, 4539844108800, 209497816281600, 10570762445443200, 578997352591257600, 34214810278128480000, 2169772724008976486400, 146984464202544531763200
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*exp(x^3)))/x))
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a(n) = sum(k=0, n\3, (n-3*k)^k*(2*n-3*k)!/(k!*(n-3*k)!))/(n+1);
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);
A371067
E.g.f. satisfies A(x) = 1 + x*exp(x^2*A(x)^2).
Original entry on oeis.org
1, 1, 0, 6, 48, 180, 2880, 46200, 483840, 9087120, 203212800, 3752511840, 89413632000, 2510276408640, 66301996400640, 1982685238934400, 67064515854336000, 2274167610024710400, 82881756045036748800, 3301346557970183923200, 135363022243685203968000
Offset: 0
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