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%I #17 Jul 07 2019 03:17:41
%S 1,1,4,2,7,6,11,8,18,16,24,23,34,36,51,48,66,74,90,98,126,137,164,182,
%T 220,247,294,324,380,434,496,556,650,728,835,938,1068,1204,1372,1531,
%U 1736,1956,2198,2462,2784,3104,3482,3890,4358,4864,5441,6048,6748,7516
%N Sum of smallest parts of all partitions of n into odd parts.
%C a(n) = Sum_{k>=1} k*A116856(n,k). - _Emeric Deutsch_, Feb 24 2006
%H Vaclav Kotesovec, <a href="/A092314/b092314.txt">Table of n, a(n) for n = 1..2500</a>
%F G.f.: Sum((2*n-1)*x^(2*n-1)/Product(1-x^(2*k-1), k = n .. infinity), n = 1 .. infinity).
%F a(n) ~ exp(Pi*sqrt(n/3)) / (4 * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 07 2019
%e a(5)=7 because the partitions of 5 into odd parts are [5],[3,1,1] and [1,1,1,1,1] and the smallest parts add up to 5+1+1=7.
%p g:=sum((2*n-1)*x^(2*n-1)/Product(1-x^(2*k-1),k=n..30),n=1..30): gser:=series(g,x=0,57): seq(coeff(gser,x^n),n=1..54); # _Emeric Deutsch_, Feb 24 2006
%t nmax = 50; Rest[CoefficientList[Series[Sum[(2*n - 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. A092322, A092269, A092309, A092321, A092313, A092310, A092311, A092268.
%Y Cf. A116856, A092322.
%K easy,nonn
%O 1,3
%A _Vladeta Jovovic_, Feb 15 2004
%E More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
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