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A066188 Sum of the second moments of all partitions of n. 1
0, 0, 1, 6, 22, 58, 141, 289, 579, 1054, 1885, 3161, 5280, 8371, 13220, 20183, 30605, 45178, 66448, 95546, 136877, 192759, 270146, 373387, 514187, 699429, 947846, 1272067, 1700456, 2254007, 2977623, 3904091, 5102058, 6625434, 8575277, 11037277, 14163777 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The first element of each partition is given weight 0.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

EXAMPLE

a(3) = 6 because the second moments of all partitions of 3 are {3}.{0},{2,1}.{0,1} and {1,1,1}.{0,1,4}, resulting in 0,1,5; summing to 6.

MAPLE

b:= proc(n, i, t) option remember; `if`(n=0, [1, 0],

      `if`(i<1, [0$2], `if`(i>n, b(n, i-1, t), b(n, i-1, t)+

       (h-> h+[0, h[1]*i*t^2])(b(n-i, i, t+1)))))

    end:

a:= n-> b(n$2, 0)[2]:

seq(a(n), n=0..50);  # Alois P. Heinz, Jan 29 2014

MATHEMATICA

Table[ Plus@@Map[ #.Range[ 0, -1+Length[ # ] ]^2&, IntegerPartitions[ n ] ], {n, 30} ]

CROSSREFS

Sequence in context: A081441 A127760 A320243 * A071239 A105450 A011888

Adjacent sequences:  A066185 A066186 A066187 * A066189 A066190 A066191

KEYWORD

easy,nonn

AUTHOR

Wouter Meeussen, Dec 15 2001

STATUS

approved

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Last modified February 23 07:31 EST 2020. Contains 332159 sequences. (Running on oeis4.)