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

1,2

Comments

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

Links

Table of n, a(n) for n=1..49.

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).

Example

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.

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);

Crossrefs

Cf. A117466, A117467, A117468.

Sequence in context: A129728 A307270 A310160 * A073359 A310161 A137041

Adjacent sequences: A117466 A117467 A117468 * A117470 A117471 A117472

Keyword

nonn

Author

Emeric Deutsch, Mar 19 2006

Status

approved