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A116684 Sum of the even parts in all partitions of n into distinct parts. 3
0, 0, 2, 2, 4, 6, 14, 18, 22, 34, 50, 66, 88, 118, 154, 202, 248, 320, 412, 512, 636, 794, 972, 1194, 1454, 1766, 2134, 2576, 3092, 3696, 4426, 5254, 6214, 7364, 8672, 10196, 11986, 14014, 16360, 19084, 22190, 25746, 29860, 34516, 39846, 45952, 52848 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n)=Sum(k*A116683(n,k), k>=0).

LINKS

Table of n, a(n) for n=0..46.

FORMULA

G.f.=2*product(1+x^j,j=1..infinity)*sum((jx^(2j)/(1+x^(2j)), j=1..infinity)).

EXAMPLE

a(9)=34 because in the partitions of 9 into distinct parts, namely, [9],[81],[72],[6,3],[6,2,1],[5,4],[5,3,1] and [4,3,2], the sum of the even parts is 8+2+6+6+2+4+4+2=34.

MAPLE

f:=2*product(1+x^j, j=1..60)*sum((j*x^(2*j)/(1+x^(2*j)), j=1..35)): fser:=series(f, x=0, 55): seq(coeff(fser, x, n), n=0..50);

MATHEMATICA

Map[Total[Select[Flatten[d[#]], EvenQ]] &, -1 + Range[30]] )

(* Peter J. C. Moses, Mar 14 2014 *)

CROSSREFS

Cf. A116681, A116682, A116683.

Sequence in context: A074028 A181926 A061894 * A276057 A116637 A153961

Adjacent sequences:  A116681 A116682 A116683 * A116685 A116686 A116687

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Feb 22 2006

STATUS

approved

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Last modified February 18 00:28 EST 2020. Contains 332006 sequences. (Running on oeis4.)