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A116682 Sum of the odd parts in all partitions of n into distinct parts. 3
0, 1, 0, 4, 4, 9, 10, 17, 26, 38, 50, 66, 92, 116, 154, 203, 264, 326, 416, 514, 644, 802, 986, 1198, 1474, 1784, 2156, 2608, 3124, 3728, 4454, 5286, 6266, 7420, 8736, 10279, 12062, 14106, 16472, 19214, 22330, 25914, 30032, 34714, 40058, 46208, 53136 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
a(n)=Sum(k*A116681(n,k), k=0..n).
LINKS
FORMULA
G.f.=product(1+x^j,j=1..infinity)*sum((2j-1)x^(2j-1)/(1+x^(2j-1)), j=1..infinity).
EXAMPLE
a(9)=38 because in the partitions of 9 into distinct parts, namely, [9],[8,1],[7,2],[6,3],[6,2,1],[5,4],[5,3,1] and [4,3,2], the sum of the odd parts is 9+1+7+3+1+5+5+3+1+3=38.
MAPLE
f:=product(1+x^j, j=1..70)*sum((2*j-1)*x^(2*j-1)/(1+x^(2*j-1)), j=1..40): fser:=series(f, x=0, 60): seq(coeff(fser, x, n), n=0..50);
MATHEMATICA
d[n_] := d[n] = Select[IntegerPartitions[n], DeleteDuplicates[#] == # &]
Map[Total[Select[Flatten[d[#]], OddQ]] &, -1 + Range[30]] (* Peter J. C. Moses, Mar 14 2014 *)
CROSSREFS
Sequence in context: A332777 A238629 A192032 * A168157 A222045 A088190
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Feb 22 2006
STATUS
approved

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Last modified July 23 20:47 EDT 2024. Contains 374565 sequences. (Running on oeis4.)