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A182724
Sum of all parts of all partitions of n minus the number of partitions of n.
2
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
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 * A374218 A342163 A098651
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Jan 30 2011
STATUS
approved