|
%I #12 Aug 17 2019 01:17:49
%S 1,0,2,1,3,6,10,15,30,54,92,160,282,492,859,1490,2570,4428,7627,13098,
%T 22421,38290,65265,111018,188475,319380,540266,912397,1538371,2589858,
%U 4353820,7309362,12255474,20523307,34328731,57357184,95733131,159626049
%N Number of compositions of n in which the largest part is equal to the number of parts.
%F G.f.: Sum_{k>=1} ((x^(k+1)-x)^k - (x^k-x)^k)/(x-1)^k.
%e a(7)=10 because we have 223, 232, 322, 133, 313, 331, 1114, 1141, 1411 and 4111.
%p G:=sum(((x^(k+1)-x)^k-(x^k-x)^k)/(x-1)^k,k=1..25):Gser:=series(G,x=0,45):seq(coeff(Gser,x^n),n=1..42); # _Emeric Deutsch_, Apr 16 2005
%Y Cf. A077229, A047993.
%K easy,nonn
%O 1,3
%A _Vladeta Jovovic_, Sep 25 2004
%E More terms from _Emeric Deutsch_, Apr 16 2005
|
