A117469 - OEIS

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

%S 1,3,6,9,13,19,24,30,42,49,61,79,92,110,144,162,195,242,278,332,405,

%T 463,546,656,759,882,1049,1205,1399,1655,1887,2181,2546,2909,3361,

%U 3880,4422,5069,5831,6641,7566,8666,9818,11159,12730,14376,16281,18465,20828

%N The largest part summed over all partitions of n in which every integer from the smallest part to the largest part occurs.

%C a(n)=Sum(k*A117468(n,k),k=1..n).

%F G.f.=sum(x^j*product(1+x^i, i=1..j-1)*[1+(1-x^j)sum(x^i/(1+x^i), i=1..j-1)]/(1-x^j)^2, j=1..infinity) (obtained by taking the derivative with respect to t of the g.f. G(t,x) of A117468 and setting t=1).

%e a(5)=13 because in the 5 (=A034296(5)) partitions in which every integer from the smallest to the largest part occurs, namely [5],[3,2],[2,2,1],[2,1,1,1] and [1,1,1,1,1], the sum of the largest parts is 5+3+2+2+1=13.

%p g:=sum(x^j*product(1+x^i,i=1..j-1)*(1+(1-x^j)*sum(x^i/(1+x^i),i=1..j-1))/(1-x^j)^2,j=1..70): gser:=series(g,x=0,60): seq(coeff(gser,x,n),n=1..55);

%Y Cf. A117466, A117467, A117468.

%K nonn

%O 1,2

%A _Emeric Deutsch_, Mar 19 2006