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

%I A364245 #8 Jul 16 2023 15:31:08
%S A364245 0,1,8,24,65,150,330,657,1274,2338,4172,7203,12171,20045,32474,51623,
%T A364245 80867,124841,190406,286857,427758,631367,923544,1339226,1926798,
%U A364245 2751094,3900931,5494411,7690923,10701618,14808183,20380969,27910066,38035633,51597166,69685656
%N A364245 Number of parts in all partitions of 2n into parts with multiplicity <= n.
%H A364245 Alois P. Heinz, <a href="/A364245/b364245.txt">Table of n, a(n) for n = 0..1000</a>
%F A364245 a(n) = A210485(2n,n).
%e A364245 a(2) = 8 = 3 + 2 + 2 + 1: [2,1,1], [2,2], [3,1], [4].
%p A364245 a:= proc(k) option remember; local b; b:=
%p A364245       proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p A364245         add((l-> l+[0, l[1]*j])(b(n-i*j, i-1)), j=0..min(n/i, k))))
%p A364245       end: b(2*k$2)[2]
%p A364245     end:
%p A364245 seq(a(n), n=0..37);
%Y A364245 Cf. A210485, A232623.
%K A364245 nonn
%O A364245 0,3
%A A364245 _Alois P. Heinz_, Jul 15 2023