A320381 Number of parts in all partitions of 2n with largest multiplicity n.

0, 1, 5, 7, 15, 18, 38, 43, 81, 101, 164, 206, 332, 405, 613, 783, 1115, 1410, 1984, 2483, 3402, 4281, 5697, 7147, 9417, 11702, 15167, 18861, 24093, 29782, 37745, 46377, 58206, 71325, 88665, 108194, 133675, 162278, 199154, 241040, 293934, 354306, 429968, 516256

Offset: 0

Author

Alois P. Heinz, Oct 11 2018

Keywords

• nonn

Examples

			a(2) = 5 = 3 + 2: [2,1,1], [2,2].
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..788 (terms 0..400 from Alois P. Heinz)

Crossrefs

Cf. A213177.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
      add((l-> [0, l[1]*j]+l)(b(n-i*j, i-1, k)), j=0..min(n/i, k))))
    end:
a:= n-> (b(2*n$2, n)-b(2*n$2, n-1))[2]:
seq(a(n), n=0..45);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n==0, {1, 0}, If[i<1, {0, 0}, Sum[b[n - i*j, i - 1, k] /. l_List :> {l[[1]], l[[2]] + l[[1]]*j}, {j, 0, Min[n/i, k]}]]];
a[n_] := (b[2n, 2n, n] - b[2n, 2n, n-1])[[2]];
a /@ Range[0, 45] (* Jean-François Alcover, Dec 14 2020, after Alois P. Heinz *)

Formula

a(n) = A213177(2n,n).