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A066184 Sum of the first moments of all partitions of n. 2
0, 1, 5, 13, 32, 61, 123, 208, 367, 590, 957, 1459, 2266, 3328, 4938, 7097, 10205, 14299, 20100, 27626, 38023, 51485, 69600, 92882, 123863, 163235, 214798, 280141, 364530, 470660, 606557, 776233, 991370, 1258827, 1594741, 2010142, 2528445 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The first element of each partition is given weight 1.

LINKS

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

FORMULA

a(n) = 1/2*(A066183(n) + A066186(n)). - Vladeta Jovovic, Mar 23 2003

EXAMPLE

a(3)=13 because the first moments of all partitions of 3 are {3}.{1},{2,1}.{1,2} and {1,1,1}.{1,2,3}, resulting in 3,4,6; summing to 13.

MAPLE

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

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

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

    end:

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

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

MATHEMATICA

Table[ Plus@@ Map[ #.Range[ Length[ # ] ]&, IntegerPartitions[ n ] ], {n, 40} ]

(* Second program: *)

b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, If[i > n, b[n, i - 1], b[n, i - 1] + Function[h, h + {0, h[[1]]*i*(i + 1)/2}][b[n - i, i]]]]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 0, 50}] (* Jean-Fran├žois Alcover, Aug 29 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A066185.

Sequence in context: A046789 A271902 A272539 * A231799 A146924 A272161

Adjacent sequences:  A066181 A066182 A066183 * A066185 A066186 A066187

KEYWORD

easy,nonn

AUTHOR

Wouter Meeussen, Dec 15 2001

STATUS

approved

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Last modified February 21 20:44 EST 2020. Contains 332111 sequences. (Running on oeis4.)