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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(n-1))*n = A138879(n) - A000041(n-1).

a(n) ~ Pi^2/6*A000070(n-2). - Peter Bala, Dec 23 2013

MATHEMATICA

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-Fran├žois 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

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Last modified December 5 15:24 EST 2016. Contains 278770 sequences.