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%I #9 Dec 13 2020 09:31:28
%S 4,0,5,5,15,16,30,36,60,75,116,149,217,273,386,491,664,839,1116,1399,
%T 1829,2292,2937,3656,4638,5729,7187,8840,10984,13430,16558,20138,
%U 24657,29846,36288,43736,52880,63430,76289,91159,109106,129841,154724,183452,217727
%N Number of parts in all partitions of n with largest multiplicity four.
%H Alois P. Heinz, <a href="/A320374/b320374.txt">Table of n, a(n) for n = 4..1000</a>
%F a(n) ~ 3^(1/4) * log(5) * exp(2*Pi*sqrt(2*n/15)) / (2^(5/4) * 5^(1/4) * 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->l+[0, l[1]*j])(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])(4):
%p seq(a(n), n=4..50);
%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 = 4}, (b[n, n, k] - b[n, n, k - 1])[[2]]];
%t a /@ Range[4, 60] (* _Jean-François Alcover_, Dec 13 2020, after _Alois P. Heinz_ *)
%Y Column k=4 of A213177.
%K nonn
%O 4,1
%A _Alois P. Heinz_, Oct 11 2018
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