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A364245
Number of parts in all partitions of 2n into parts with multiplicity <= n.
2
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
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
Sequence in context: A208895 A111071 A090336 * A200253 A343546 A199911
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 15 2023
STATUS
approved