A305991
Expansion of (1-27*x)^(1/9).
Original entry on oeis.org
1, -3, -36, -612, -11934, -250614, -5513508, -125235396, -2911722957, -68910776649, -1653858639576, -40143659706072, -983519662798764, -24285370135261788, -603664914790793016, -15091622869769825400, -379177024602966863175, -9568643738510163782475
Offset: 0
(1-b*x)^(1/
A003557(b)):
A002420 (b=4),
A004984 (b=8),
A004990 (b=9), (-1)^n *
A108735 (b=12),
A301271 (b=16), (-1)^n *
A108733 (b=18),
A049393 (b=25), this sequence (b=27),
A004996 (b=36),
A303007 (b=240),
A303055 (b=504),
A305886 (b=1728).
A386416
G.f. A(x) satisfies A(x) = (1 + 9*x*A(x)^8)^(1/3).
Original entry on oeis.org
1, 3, 63, 1881, 65610, 2499336, 100777122, 4228144596, 182674383705, 8072369224920, 363154406671485, 16576444298006658, 765806677899249168, 35739548618003938440, 1682429522012566325460, 79793991407758199002740, 3809208342822290233767522, 182890356905449116974950200
Offset: 0
-
A386416[n_] := 9^n*Binomial[(8*n + 1)/3, n]/(8*n + 1);
Array[A386416, 20, 0] (* Paolo Xausa, Aug 01 2025 *)
-
apr(n, p, r) = r*binomial(n*p+r, n)/(n*p+r);
a(n) = 9^n*apr(n, 8/3, 1/3);
A380029
Expansion of e.g.f. (1 - 3*x*exp(x))^(1/3).
Original entry on oeis.org
1, -1, -4, -25, -252, -3545, -63806, -1397781, -36069272, -1071165745, -35977484250, -1348257912221, -55766033179220, -2523251585908521, -123972318738063446, -6572554273909419685, -373979858167243433136, -22731929051273411113313, -1470009560015441800798514
Offset: 0