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A117469 The largest part summed over all partitions of n in which every integer from the smallest part to the largest part occurs. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 18 01:05 EDT 2019. Contains 325109 sequences. (Running on oeis4.)