A370985
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^3*exp(x)) ).
Original entry on oeis.org
1, 0, 0, 6, 24, 60, 3000, 45570, 403536, 10644984, 297562320, 5517833310, 142801022760, 5076208052916, 150282366476424, 4713707747551530, 189345734667052320, 7517503455423740400, 295622259241028433696, 13370535071068474177974, 642403497550155241197240
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^3*exp(x)))/x))
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a(n) = sum(k=0, n\3, k^(n-3*k)*(n+k)!/(k!*(n-3*k)!))/(n+1);
A370927
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x^2)) ).
Original entry on oeis.org
1, 1, 4, 36, 480, 8460, 187200, 4998000, 156387840, 5614313040, 227520921600, 10275211679040, 511772590264320, 27870149349282240, 1647541857684602880, 105073768465758892800, 7191330561736409088000, 525746801445336504633600
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*exp(x^2)))/x))
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a(n) = sum(k=0, n\2, (n-2*k)^k*(2*n-2*k)!/(k!*(n-2*k)!))/(n+1);
A371068
E.g.f. satisfies A(x) = 1 + x*exp(x^3*A(x)^3).
Original entry on oeis.org
1, 1, 0, 0, 24, 360, 2160, 7560, 241920, 8164800, 145756800, 1736380800, 34488115200, 1416906691200, 46117316044800, 1085696644032000, 26627911620710400, 1054301997805056000, 46867776416068608000, 1726488804870679449600, 58404671366139850752000
Offset: 0
A376347
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x^3) - 1)) ).
Original entry on oeis.org
1, 0, 0, 0, 24, 0, 0, 2520, 201600, 0, 604800, 259459200, 16765056000, 259459200, 406832025600, 100037089152000, 5963169474662400, 844757641728000, 560207699251200000, 107716905363549081600, 6157546579533533184000, 3525275009847951360000, 1582967914636148232192000, 264668100119565849907200000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x^3)-1)))/x))
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a(n) = sum(k=0, n\3, (2*n-3*k)!*stirling(k, n-3*k, 2)/k!)/(n+1);
Showing 1-4 of 4 results.