A238517 Square row sums of the table A008289 (A060016).

1, 1, 1, 2, 2, 5, 6, 11, 14, 26, 34, 52, 79, 110, 162, 231, 328, 446, 660, 872, 1236, 1660, 2327, 3060, 4238, 5586, 7595, 9988, 13376, 17470, 23318, 30286, 39744, 51676, 67276, 86929, 112390, 144472, 185428, 237826, 303171, 386468, 490838, 622882, 786068, 995118, 1249838, 1573522, 1970542

Offset: 0

Author

Emanuele Munarini, Feb 28 2014

Keywords

• nonn

Crossrefs

Cf. A008289, A060016.

Programs

Mathematica

qq[n_] := CoefficientList[Series[Sum[x^Binomial[k+1,2]y^k/Product[1-x^i,{i,1,k}],{k,0,n}],{x,0,n},{y,0,n}],{x,y}]
Total[Transpose[Map[#^2 &, qq[100]]]]

Formula

a(n) = sum(q(n,k)^k,k=0..n), where q(n,k) is the number of partitions of n into k distinct parts (A008289, A060016).