A238313 Alternating square row sums of the table A072233 (A008284).

1, 1, 0, 1, 3, 1, 3, 3, 10, 18, 12, 26, 39, 57, 59, 116, 201, 219, 325, 416, 625, 810, 1074, 1447, 2345, 3078, 3530, 5084, 6790, 9063, 11674, 15580, 20887, 27537, 33640, 45065, 61297, 76883, 96889, 126243, 169268, 210005, 262068, 337445, 438197, 552346, 686794, 865904, 1128611, 1407533, 1732572

Offset: 0

Author

Emanuele Munarini, Feb 24 2014

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..90

Crossrefs

Cf. A072233, A008284.

Programs

Mathematica

pnkList[n_] := Table[Length[IntegerPartitions[n, {k}]], {k,0,n}]
Table[Total[Table[(-1)^(n-k),{k,0,n}] Map[#^2 &, pnkList[n]]], {n,0,50}]

Formula

a(n) = sum((-1)^(n-k)*p(n,k)^2,k=0..n), where p(n,k) is the number of partitions of n into k positive parts (A072233, A008284).