A182724 - OEIS

%I #14 Jan 17 2015 09:36:10

%S 0,2,6,15,28,55,90,154,240,378,560,847,1212,1755,2464,3465,4752,6545,

%T 8820,11913,15840,21042,27610,36225,46992,60900,78260,100386,127820,

%U 162516,205260,258819,324576,406230,506022,629195,778932,962555,1185030

%N Sum of all parts of all partitions of n minus the number of partitions of n.

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

%H Harvey P. Dale, <a href="/A182724/b182724.txt">Table of n, a(n) for n = 1..1000</a>

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

%e 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.

%p a:= n-> (n-1) *combinat[numbpart](n):

%p seq (a(n), n =1..50);

%t pnxt[n_]:=Module[{ps=IntegerPartitions[n]},Total[Flatten[ps]]- Length[ps]]; Array[pnxt,40] (* _Harvey P. Dale_, Jul 15 2011 *)

%t Table[(n-1)PartitionsP[n],{n,40}] (* _Harvey P. Dale_, Jan 17 2015 *)

%Y Cf. A000041, A066186. Column 1 of A182729.

%K nonn,easy

%O 1,2

%A _Omar E. Pol_, Jan 30 2011