A365283
E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x^2*A(x)^2).
Original entry on oeis.org
1, 1, 2, 12, 120, 1380, 19440, 341040, 7029120, 164762640, 4355769600, 128527439040, 4181332700160, 148633442717760, 5734427199621120, 238676208285715200, 10659325532663808000, 508452777299622355200, 25800664274991135129600
Offset: 0
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Join[{1},Table[n!/(n+1) * Sum[(n-2*k)^k * Binomial[n+1,n-2*k]/k!, {k, 0, Floor[n/2]}], {n,1,20}]] (* Vaclav Kotesovec, Nov 08 2023 *)
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a(n) = n!*sum(k=0, n\2, (n-2*k)^k*binomial(n+1, n-2*k)/k!)/(n+1);
A371019
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, 2280, 35490, 322896, 6532344, 175392720, 3351681630, 74021715240, 2328376978356, 68824597123464, 1989994550546730, 69687384248405280, 2634948077918611440, 98220733842576688416, 3966108617957749165494, 175679596523004500742840
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) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n+1, k)/(n-3*k)!)/(n+1);
A365285
E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x^3*A(x)).
Original entry on oeis.org
1, 1, 2, 6, 48, 480, 5040, 57960, 806400, 13426560, 250992000, 5102697600, 113283878400, 2760905347200, 73287883468800, 2093750122464000, 63947194517606400, 2082970788291993600, 72182922107859763200, 2651026034089585152000
Offset: 0
A365286
E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x^3*A(x)^2).
Original entry on oeis.org
1, 1, 2, 6, 48, 600, 7920, 108360, 1693440, 32114880, 715478400, 17616614400, 467505561600, 13438170345600, 421361740800000, 14345678194848000, 524464774215782400, 20420391682852761600, 844038690729589555200, 36981569420732192256000
Offset: 0
A370926
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x*exp(x^3/6)) ).
Original entry on oeis.org
1, 1, 2, 6, 28, 220, 2520, 34510, 519680, 8527680, 154831600, 3151456000, 71830281600, 1809141934600, 49559087177600, 1459865188782000, 45970426027926400, 1543274016213529600, 55120521154277779200, 2088917638216953544000, 83717918489664018560000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1+x*exp(x^3/6)))/x))
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a(n) = n!*sum(k=0, n\3, (n-3*k)^k*binomial(n+1, n-3*k)/(6^k*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
Showing 1-6 of 6 results.