A117953 - OEIS

%I #3 Mar 30 2012 17:36:09

%S 1,1,0,1,1,1,2,2,2,3,4,4,4,5,7,8,9,10,12,14,16,19,21,24,28,32,36,41,

%T 47,53,59,67,76,85,96,108,121,135,151,169,188,210,235,261,289,322,357,

%U 395,438,485,536,592,654,721,795,876,963,1059,1165,1279,1405,1541,1688,1851

%N Number of partitions of n into odd parts and such that parts having size k occur at most k times.

%F G.f.=product((1-x^(2k(2k-1)))/(1-x^(2k-1)), k=1..infinity).

%e a(10)=4 because we have [9,1],[7,3],[5,5] and [3,3,3,1].

%p g:=product((1-x^(2*k*(2*k-1)))/(1-x^(2*k-1)),k=1..50): gser:=series(g,x=0,70): seq(coeff(gser,x,n),n=0..67);

%K nonn

%O 0,7

%A _Emeric Deutsch_, Apr 05 2006