A182711 -id:A182711 - cp's OEIS frontend

A138880 Sum of all parts of all partitions of n that do not contain 1 as a part.

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

Offset: 1

Omar E. Pol, Apr 30 2008

nonn

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

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Cf. A000041, A002865, A066186, A133041, A138135, A138136, A138137, A138138, A138151, A138879, A139100.

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

a(n) = A002865(n)*n = (A000041(n) - A000041(n-1))*n = A138879(n) - A000041(n-1).
a(n) ~ Pi^2/6*A000070(n-2). - 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
a(n) ~ Pi * exp(sqrt(2*n/3)*Pi) / (12*sqrt(2*n)) * (1 - (3*sqrt(3/2)/Pi + 13*Pi/(24*sqrt(6)))/sqrt(n) + (217*Pi^2/6912 + 9/(2*Pi^2) + 13/8)/n). - Vaclav Kotesovec, Jul 06 2019

Better definition from Omar E. Pol, Sep 23 2013

A182710 Triangle read by rows in which row n lists the parts >= 2 of the last section of the set of partitions of n, in the order produced by the shell model of partitions of A138121, with a(1)=0.

Original entry on oeis.org

0, 2, 3, 4, 2, 2, 5, 3, 2, 6, 3, 3, 4, 2, 2, 2, 2, 7, 4, 3, 5, 2, 3, 2, 2, 8, 4, 4, 5, 3, 6, 2, 3, 3, 2, 4, 2, 2, 2, 2, 2, 2, 9, 5, 4, 6, 3, 3, 3, 3, 7, 2, 4, 3, 2, 5, 2, 2, 3, 2, 2, 2

Offset: 1

Omar E. Pol, Nov 28 2010

These are the parts located in the "head" of the last section.

For other versions see A138136 and A182711.

			Triangle begins:
0,
2,
3,
4,2,2,
5,3,2,
6,3,3,4,2,2,2,2,
7,4,3,5,2,3,2,2,
8,4,4,5,3,6,2,3,3,2,4,2,2,2,2,2,2,
9,5,4,6,3,3,3,3,7,2,4,3,2,5,2,2,3,2,2,2

Omar E. Pol, Illustration of the shell model of partitions (3D view)
Omar E. Pol, Illustration. How to build the last section of the set of partitions of n: copy, paste and fill.

Cf. A135010, A138121, A138136, A182711.

cp's OEIS Frontend

A138880 Sum of all parts of all partitions of n that do not contain 1 as a part.

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