%I #11 Aug 17 2019 01:17:33

%S 0,1,1,4,8,17,38,83,174,367,771,1606,3324,6849,14054,28743,58605,

%T 119161,241717,489345,988945,1995604,4021710,8095815,16281400,

%U 32716231,65694106,131833462,264423116,530128036,1062424867,2128513095

%N Number of compositions of n where the largest part is less than the number of parts.

%F G.f.: Sum_{k>=0} ((x^k-x)/(x-1))^k.

%e a(5)=8 because we have 1112, 1121, 1211, 2111, 122, 212, 221 and 11111.

%p 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

%Y Cf. A077229, A047993, A064173, A064174.

%K easy,nonn

%O 1,4

%A _Vladeta Jovovic_, Sep 25 2004

%E More terms from _Emeric Deutsch_, Apr 16 2005