A365287
E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x^3*A(x)^3).
Original entry on oeis.org
1, 1, 2, 6, 48, 720, 11520, 183960, 3185280, 65681280, 1637193600, 46436544000, 1423113753600, 46607434473600, 1648149184281600, 63369409495392000, 2634451417524326400, 117088187211284889600, 5518546983426135859200, 275022667579200532992000
Offset: 0
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Join[{1},Table[n!/(n+1) * Sum[(n-3*k)^k * Binomial[n+1,n-3*k]/k!, {k,0,Floor[n/3]}], {n,1,20}]] (* Vaclav Kotesovec, Nov 08 2023 *)
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a(n) = n!*sum(k=0, n\3, (n-3*k)^k*binomial(n+1, n-3*k)/k!)/(n+1);
A365282
E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x^2*A(x)).
Original entry on oeis.org
1, 1, 2, 12, 96, 900, 10800, 157080, 2634240, 50455440, 1089849600, 26157479040, 690848040960, 19924295751360, 623024501299200, 20996216063222400, 758724126031872000, 29267547577396128000, 1200407895406514995200
Offset: 0
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Join[{1}, Table[n! * Sum[(n-2*k)^k * Binomial[n-k+1,n-2*k] / ((n-k+1)*k!), {k,0,Floor[n/2]}], {n,1,20}]] (* Vaclav Kotesovec, Aug 31 2023 *)
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a(n) = n!*sum(k=0, n\2, (n-2*k)^k*binomial(n-k+1, n-2*k)/((n-k+1)*k!));
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
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
Showing 1-4 of 4 results.