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A320381 Number of parts in all partitions of 2n with largest multiplicity n. 2
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 (list; graph; refs; listen; history; text; internal format)
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).

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-Fran├žois 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

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Last modified June 13 05:21 EDT 2021. Contains 344981 sequences. (Running on oeis4.)