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%I #11 Dec 13 2020 09:31:11
%S 2,0,5,6,9,13,23,30,44,58,85,108,149,191,258,326,425,532,688,852,1082,
%T 1331,1670,2042,2531,3068,3771,4554,5543,6653,8051,9607,11543,13722,
%U 16377,19390,23023,27132,32073,37660,44303,51834,60744,70813,82666,96082,111759
%N Number of parts in all partitions of n with largest multiplicity two.
%H Alois P. Heinz, <a href="/A320372/b320372.txt">Table of n, a(n) for n = 2..5000</a>
%F a(n) ~ log(3) * exp(2*Pi*sqrt(n)/3) / (2*Pi*n^(1/4)). - _Vaclav Kotesovec_, Oct 25 2018
%p b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p add((l-> [0, l[1]*j]+l)(b(n-i*j, i-1, k)), j=0..min(n/i, k))))
%p end:
%p a:= n-> (k-> (b(n$2, k)-b(n$2, k-1))[2])(2):
%p seq(a(n), n=2..60);
%t b[n_, i_, k_] := b[n, i, k] = If[n==0, {1, 0}, If[i<1, {0, 0}, Sum[ Function[l, {0, l[[1]]*j} + l][b[n - i j, i-1, k]], {j, 0, Min[n/i, k]}]]];
%t a[n_] := With[{k = 2}, (b[n, n, k] - b[n, n, k - 1])[[2]]];
%t a /@ Range[2, 60] (* _Jean-François Alcover_, Dec 13 2020, after _Alois P. Heinz_ *)
%Y Column k=2 of A213177.
%K nonn
%O 2,1
%A _Alois P. Heinz_, Oct 11 2018
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