A238314 Binomial transform of the squared rows of the table A072233 (A008284).

1, 1, 3, 7, 33, 91, 388, 1163, 4231, 13297, 44694, 136621, 444535, 1335335, 4149785, 12327698, 37154245, 108185961, 318923590, 913506701, 2633793550, 7443298426, 21073435606, 58715695683, 163805615535, 450730653566, 1239947467778, 3374934052348

Offset: 0

Author

Emanuele Munarini, Feb 24 2014

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..80

Crossrefs

Cf. A072233, A008284.

Programs

Mathematica

pnkList[n_] := Table[Length[IntegerPartitions[n, {k}]], {k, 0, n}]
Table[Total[Table[Binomial[n,k],{k,0,n}] Map[#^2 &, pnkList[n]]], {n,0,40}]

Formula

a(n) = sum(binomial(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).