A117469 The largest part summed over all partitions of n in which every integer from the smallest part to the largest part occurs.
1, 3, 6, 9, 13, 19, 24, 30, 42, 49, 61, 79, 92, 110, 144, 162, 195, 242, 278, 332, 405, 463, 546, 656, 759, 882, 1049, 1205, 1399, 1655, 1887, 2181, 2546, 2909, 3361, 3880, 4422, 5069, 5831, 6641, 7566, 8666, 9818, 11159, 12730, 14376, 16281, 18465, 20828
Offset: 1
Keywords
Examples
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.
Programs
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Maple
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);
Formula
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).
Comments