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

0,3

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A213177.

Sequence in context: A031069 A314364 A321130 * A309292 A050851 A058918

Adjacent sequences: A320378 A320379 A320380 * A320382 A320383 A320384

Keyword

nonn

Author

Alois P. Heinz, Oct 11 2018

Status

approved