A364245 Number of parts in all partitions of 2n into parts with multiplicity <= n.

0, 1, 8, 24, 65, 150, 330, 657, 1274, 2338, 4172, 7203, 12171, 20045, 32474, 51623, 80867, 124841, 190406, 286857, 427758, 631367, 923544, 1339226, 1926798, 2751094, 3900931, 5494411, 7690923, 10701618, 14808183, 20380969, 27910066, 38035633, 51597166, 69685656

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) = A210485(2n,n).

Example

a(2) = 8 = 3 + 2 + 2 + 1: [2,1,1], [2,2], [3,1], [4].

Maple

a:= proc(k) option remember; local b; b:=
      proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
        add((l-> l+[0, l[1]*j])(b(n-i*j, i-1)), j=0..min(n/i, k))))
      end: b(2*k$2)[2]
    end:
seq(a(n), n=0..37);

Crossrefs

Cf. A210485, A232623.

Sequence in context: A208895 A111071 A090336 * A200253 A343546 A199911

Adjacent sequences: A364242 A364243 A364244 * A364246 A364247 A364248

Keyword

nonn

Author

Alois P. Heinz, Jul 15 2023

Status

approved