

A138880


Sum of all parts of all partitions of n that do not contain 1 as a part.


19



0, 2, 3, 8, 10, 24, 28, 56, 72, 120, 154, 252, 312, 476, 615, 880, 1122, 1584, 1995, 2740, 3465, 4620, 5819, 7680, 9575, 12428, 15498, 19824, 24563, 31170, 38378, 48224, 59202, 73678, 90055, 111384, 135420, 166364, 201630, 246120, 297045, 360822
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Sum of all parts > 1 of the last section of the set of partitions of n.
Row sums of triangle A182710. Also row sums of other similar triangles as A138136 and A182711.
Partial sums give A194552.  Omar E. Pol, Sep 23 2013


LINKS

Table of n, a(n) for n=1..42.


FORMULA

a(n) = A002865(n)*n = (A000041(n)  A000041(n1))*n = A138879(n)  A000041(n1).
a(n) ~ Pi^2/6*A000070(n2).  Peter Bala, Dec 23 2013
G.f.: x*f'(x), where f(x) = Product_{k>=2} 1/(1  x^k).  Ilya Gutkovskiy, Apr 13 2017


MATHEMATICA

Table[Total[Flatten[Select[IntegerPartitions[n], FreeQ[#, 1]&]]], {n, 50}] (* Harvey P. Dale, May 24 2015 *)
a[n_] := (PartitionsP[n]  PartitionsP[n1])*n; Table[a[n], {n, 1, 50}] (* JeanFrançois Alcover, Oct 07 2015 *)


CROSSREFS

Cf. A000041, A002865, A066186, A133041, A138135, A138136, A138137, A138138, A138151, A138879, A139100.
Sequence in context: A098844 A034437 A175715 * A063474 A163492 A025562
Adjacent sequences: A138877 A138878 A138879 * A138881 A138882 A138883


KEYWORD

nonn


AUTHOR

Omar E. Pol, Apr 30 2008


EXTENSIONS

Better definition from Omar E. Pol, Sep 23 2013


STATUS

approved



