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A235792 Total number of parts in all overpartitions of n.

%I A235792 #26 Apr 13 2025 10:12:11
%S A235792 2,6,16,34,68,128,228,390,650,1052,1664,2584,3940,5916,8768,12826,
%T A235792 18552,26566,37672,52956,73848,102192,140420,191688,260038,350700,
%U A235792 470384,627604,833236,1101080,1448500,1897438,2475464,3217016,4165200,5373714,6909180,8854288
%N A235792 Total number of parts in all overpartitions of n.
%C A235792 It appears that a(n) is also the sum of largest parts of all overpartitions of n.
%C A235792 More generally, It appears that the total number of parts >= k in all overpartitions of n equals the sum of k-th largest parts of all overpartitions of n. In this case k = 1. Also the first column of A235797.
%C A235792 The equivalent sequence for partitions is A006128.
%H A235792 Vaclav Kotesovec, <a href="/A235792/b235792.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Alois P. Heinz)
%F A235792 log(a(n)) ~ Pi*sqrt(n). - _Vaclav Kotesovec_, Apr 13 2025
%p A235792 b:= proc(n, i) option remember; `if`(n=0, [1, 0],
%p A235792       `if`(i<1, [0$2], b(n, i-1)+add((l-> l+[0, l[1]*j])
%p A235792        (2*b(n-i*j, i-1)), j=1..n/i)))
%p A235792     end:
%p A235792 a:= n-> b(n$2)[2]:
%p A235792 seq(a(n), n=1..40);  # _Alois P. Heinz_, Jan 21 2014
%t A235792 b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i<1, {0, 0}, b[n, i-1] + Sum[ Function[l, l+{0, l[[1]]*j}][2*b[n-i*j, i-1]], {j, 1, n/i}]]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Nov 11 2015, after _Alois P. Heinz_ *)
%Y A235792 Cf. A006128, A015128, A211971, A235790, A235793, A235797, A235798, A236000, A236001.
%K A235792 nonn
%O A235792 1,1
%A A235792 _Omar E. Pol_, Jan 18 2014
%E A235792 More terms from _Alois P. Heinz_, Jan 21 2014