A182724 Sum of all parts of all partitions of n minus the number of partitions of n.

0, 2, 6, 15, 28, 55, 90, 154, 240, 378, 560, 847, 1212, 1755, 2464, 3465, 4752, 6545, 8820, 11913, 15840, 21042, 27610, 36225, 46992, 60900, 78260, 100386, 127820, 162516, 205260, 258819, 324576, 406230, 506022, 629195, 778932, 962555, 1185030

Offset

1,2

Comments

a(n) is the sum of (the zeroth moments of) all partitions of n minus the partition number of n.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = (n-1)*A000041(n) = A066186(n) - A000041(n).

Example

a(7) = 90 = (7-1)*15 = 105 - 15, because the number of partitions of 7 is 15 and the sum of all parts of all partitions of 7 is 7*15 = 105.

Maple

a:= n-> (n-1) *combinat[numbpart](n):
seq (a(n), n =1..50);

Mathematica

pnxt[n_]:=Module[{ps=IntegerPartitions[n]}, Total[Flatten[ps]]- Length[ps]]; Array[pnxt, 40] (* Harvey P. Dale, Jul 15 2011 *)
Table[(n-1)PartitionsP[n], {n, 40}] (* Harvey P. Dale, Jan 17 2015 *)

Crossrefs

Cf. A000041, A066186. Column 1 of A182729.

Sequence in context: A163061 A331773 A033286 * A342163 A098651 A087427

Adjacent sequences: A182721 A182722 A182723 * A182725 A182726 A182727

Keyword

nonn,easy

Author

Omar E. Pol, Jan 30 2011

Status

approved