A377829
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x)/(1 + x)^2 ).
Original entry on oeis.org
1, 3, 25, 364, 7713, 216216, 7568041, 318256800, 15644919681, 880848974080, 55912403743161, 3951344780946432, 307737594185310625, 26190457718737019904, 2418475248758250599625, 240846113359411822759936, 25731326615411044591298049, 2935802801104074173428531200
Offset: 0
A382037
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * B(x)^3) ), where B(x) = 1 + x*B(x)^3 is the g.f. of A001764.
Original entry on oeis.org
1, 1, 9, 160, 4325, 157896, 7280077, 406085632, 26599741065, 2001864880000, 170236619802161, 16144762562002944, 1689534516295056301, 193403842876754728960, 24040636567791329323125, 3224829927677539092791296, 464325325579881390473331473, 71428455280041816247241637888
Offset: 0
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a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (n+1)^(n-k-1)*binomial(3*n, k)/(n-k-1)!));
A380647
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-3*x)/(1 + x)^3 ).
Original entry on oeis.org
1, 6, 105, 3246, 146637, 8780688, 657224901, 59140486800, 6223651526457, 750357182131200, 102014741343847329, 15443915464974191616, 2576937457466957107845, 469914373917914931984384, 92982800086882512621716925, 19843243096453465663599962112, 4543276116844426827394718716401
Offset: 0
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nmax=17; CoefficientList[(1/x)InverseSeries[Series[x*Exp[-3*x]/(1 + x)^3 ,{x,0,nmax}]],x]Range[0,nmax-1]! (* Stefano Spezia, Feb 06 2025 *)
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a(n) = 3*n!*sum(k=0, n, (3*n+3)^(k-1)*binomial(3*n+3, n-k)/k!);
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