A380516
Expansion of e.g.f. exp(x*G(x)^4) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
Original entry on oeis.org
1, 1, 9, 157, 4129, 146001, 6502681, 349790029, 22069858497, 1598577634369, 130757736096361, 11922399644742621, 1199121973234651489, 131887738425602277457, 15748194681225620534649, 2028885239529647188594381, 280525944581514367875035521, 41434950383158772951280658689
Offset: 0
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Join[{1}, Table[(n-1)! * LaguerreL[n-1, 3*n+1, -1], {n, 1, 20}]] (* Vaclav Kotesovec, Jan 26 2025 *)
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a(n) = if(n==0, 1, (n-1)!*pollaguerre(n-1, 3*n+1, -1));
A382033
E.g.f. A(x) satisfies A(x) = exp(x*B(x*A(x))^3), where B(x) = 1 + x*B(x)^3 is the g.f. of A001764.
Original entry on oeis.org
1, 1, 7, 109, 2653, 88261, 3731581, 191571493, 11576241769, 804996352873, 63324553740121, 5559962513556001, 539015912053933645, 57188111522488589293, 6591136171961660099509, 820029701725988751533341, 109537705061927547203868241, 15635869913619342121140932689
Offset: 0
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a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (k+1)^(n-k-1)*binomial(3*n, k)/(n-k-1)!));
A382032
E.g.f. A(x) satisfies A(x) = exp(x*C(x*A(x))^2), where C(x) = 1 + x*C(x)^2 is the g.f. of A000108.
Original entry on oeis.org
1, 1, 5, 55, 937, 21741, 639841, 22839139, 958882289, 46304377849, 2528571710881, 154076164781991, 10364272238514217, 762867688235619877, 60989719558159065857, 5263030218009265964011, 487578723768665716788961, 48266847740986728218648433, 5084697384633390178057209793
Offset: 0
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a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (k+1)^(n-k-1)*binomial(2*n, k)/(n-k-1)!));
A382038
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * B(x)^4) ), where B(x) = 1 + x*B(x)^4 is the g.f. of A002293.
Original entry on oeis.org
1, 1, 11, 244, 8285, 381096, 22175167, 1562582848, 129381990201, 12313784396800, 1324663415429651, 158957183013686784, 21051725357219126869, 3050121640032545419264, 479928476696367747954375, 81499293517054315684642816, 14856515462975583258374526833, 2893604521320117995839047401472
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(4*n, k)/(n-k-1)!));
A382059
E.g.f. A(x) satisfies A(x) = exp(x*B(x*A(x))^3), where B(x) = 1 + x*B(x)^4 is the g.f. of A002293.
Original entry on oeis.org
1, 1, 7, 127, 3733, 152161, 7939261, 505087843, 37920697753, 3281899787137, 321700411900441, 35227497466867531, 4262151791317099285, 564639582580738851265, 81290104199287214904037, 12637400195063381931755731, 2109868901338065949399370161, 376504852688521502050554789889
Offset: 0
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a(n) = if(n==0, 1, 3*n!*sum(k=0, n-1, (k+1)^(n-k-1)*binomial(3*n+k, k)/((3*n+k)*(n-k-1)!)));
Showing 1-5 of 5 results.