A228816 Sum of all parts of all partitions of n that contain 1 as a part.

1, 2, 6, 12, 25, 42, 77, 120, 198, 300, 462, 672, 1001, 1414, 2025, 2816, 3927, 5346, 7315, 9800, 13167, 17424, 23046, 30120, 39375, 50908, 65772, 84280, 107822, 136950, 173724, 218944, 275517, 344862, 430850, 535788, 665149, 822206, 1014585, 1247400

Offset: 1

Author

Omar E. Pol, Sep 23 2013

Keywords

• nonn

Crossrefs

Column 1 of A182701.

Cf. A000041, A000070, A066186, A138880, A194552, A228823.

Programs

Mathematica

Table[Total[Flatten[Select[IntegerPartitions[n],MemberQ[#,1]&]]],{n,40}] (* Harvey P. Dale, Sep 27 2015 *)

Formula

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

a(n) = A066186(n-1) + A000041(n-1), n >= 2.

a(n) = A194552(n-1) + A000070(n-1), n >= 2.