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Sum of smallest parts (counted with multiplicity) of all partitions of n into odd parts.
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%I #12 Jul 07 2019 03:20:28

%S 1,2,6,5,12,16,21,22,43,46,60,75,92,119,164,167,220,276,320,390,491,

%T 562,665,796,949,1109,1342,1530,1804,2144,2442,2843,3342,3837,4471,

%U 5147,5894,6780,7841,8910,10204,11718,13282,15168,17337,19594,22225,25210

%N Sum of smallest parts (counted with multiplicity) of all partitions of n into odd parts.

%H Vaclav Kotesovec, <a href="/A092313/b092313.txt">Table of n, a(n) for n = 1..2500</a>

%F G.f.: Sum((2*n-1)*x^(2*n-1)/(1-x^(2*n-1))/Product(1-x^(2*k-1), k = n .. infinity), n = 1 .. infinity).

%F a(n) ~ 3^(1/4) * exp(Pi*sqrt(n/3)) / (2*Pi*n^(1/4)). - _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+3*1+2*3+1*1=16.

%t nmax = 50; Rest[CoefficientList[Series[Sum[(2*n - 1)*x^(2*n - 1)/(1 - x^(2*n - 1)) / Product[(1 - x^(2*k - 1)), {k, n, nmax}], {n, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Jul 06 2019 *)

%Y Cf. A092314, A092322, A092269, A092309, A092321, A092310, A092311, 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