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%I #14 Apr 24 2023 12:24:17
%S 1,2,4,5,7,10,12,14,19,23,26,33,38,44,56,63,71,88,99,114,138,155,176,
%T 208,237,269,314,357,402,468,529,594,686,772,873,999,1119,1260,1431,
%U 1608,1804,2039,2284,2554,2884,3219,3590,4032,4493,5011,5603,6231,6928
%N Total number of largest parts in all partitions of n into odd parts.
%H Vaclav Kotesovec, <a href="/A092311/b092311.txt">Table of n, a(n) for n = 1..2500</a>
%F G.f.: Sum((x^(2*n-1)/(1-x^(2*n-1)))/Product((1-x^(2*k-1)), k=1..n), n=1..infinity).
%F a(n) ~ exp(Pi*sqrt(n/3)) / (4 * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 07 2019
%e Partitions of 6 into odd parts are: [1,1,1,1,1,1], [1,1,1,3], [3,3], [1,5]; thus a(6)=6+1+2+1=10.
%t nmax = 50; Rest[CoefficientList[Series[Sum[(x^(2*n - 1)/(1 - x^(2*n - 1))) / Product[(1 - x^(2*k - 1)), {k, 1, n}], {n, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Jul 06 2019 *)
%t lpp[k_]:=Module[{c=Max[k]},Count[k,c]]; Table[Total[lpp/@Select[IntegerPartitions[ n],AllTrue[ #,OddQ]&]],{n, 60}] (* _Harvey P. Dale_, Apr 24 2023 *)
%Y Cf. A092314, A092322, A092269, A092309, A092321, A092313, A092310, A092268.
%K easy,nonn
%O 1,2
%A _Vladeta Jovovic_, Feb 16 2004
%E More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
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