A098125 Number of compositions of n where the largest part is less than the number of parts.
0, 1, 1, 4, 8, 17, 38, 83, 174, 367, 771, 1606, 3324, 6849, 14054, 28743, 58605, 119161, 241717, 489345, 988945, 1995604, 4021710, 8095815, 16281400, 32716231, 65694106, 131833462, 264423116, 530128036, 1062424867, 2128513095
Offset: 1
Examples
a(5)=8 because we have 1112, 1121, 1211, 2111, 122, 212, 221 and 11111.
Programs
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Maple
G:=sum(((x^k-x)/(x-1))^k,k=0..45): Gser:=series(G,x=0,40): seq(coeff(Gser,x^n),n=1..36); # Emeric Deutsch, Apr 16 2005
Formula
G.f.: Sum_{k>=0} ((x^k-x)/(x-1))^k.
Extensions
More terms from Emeric Deutsch, Apr 16 2005