A362205
Expansion of e.g.f. exp(x/(1-3*x)^(1/3)).
Original entry on oeis.org
1, 1, 3, 19, 185, 2401, 38731, 745123, 16630769, 422157025, 12005107091, 377957000851, 13048046175913, 490052749100929, 19890724260375515, 867582126490694371, 40467070835396193761, 2009901604798183428673, 105901641663222888913699
Offset: 0
A382643
Expansion of e.g.f. exp( x/(1-3*x)^(4/3) ).
Original entry on oeis.org
1, 1, 9, 109, 1697, 32401, 733081, 19167709, 568351169, 18833921857, 689436160361, 27616959669421, 1201138514382049, 56349982190989969, 2835621797645900537, 152321976433436677981, 8697876904012444443521, 526015632425455532060929, 33581536744768011688139209
Offset: 0
A382652
Expansion of e.g.f. exp( x/(1-3*x)^(5/3) ).
Original entry on oeis.org
1, 1, 11, 151, 2601, 54401, 1341571, 38115351, 1225252561, 43935295681, 1737463744251, 75075845199191, 3517448555579641, 177538212306653121, 9600694935999031411, 553606933661659742551, 33899768045328467219361, 2196417680635853609034881, 150094038119761737476004331
Offset: 0
-
exp(x/(1-3*x)^(5/3)) ;
taylor(%,x=0,60) ;
L := gfun[seriestolist](%) ;
seq( op(i,L)*(i-1)!,i=1..nops(L)) ; # R. J. Mathar, Apr 08 2025
-
a(n) = n!*sum(k=0, n, 3^(n-k)*binomial(n+2*k/3-1, n-k)/k!);
Showing 1-3 of 3 results.