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Sum of largest parts of all partitions of n into odd parts.
11

%I #16 Jul 07 2019 03:03:02

%S 1,1,4,4,9,12,19,24,36,48,64,83,108,140,179,224,280,352,432,532,652,

%T 795,960,1160,1392,1669,1992,2368,2804,3320,3908,4592,5388,6300,7349,

%U 8560,9940,11524,13340,15401,17752,20436,23472,26920,30840,35256,40252,45900

%N Sum of largest parts of all partitions of n into odd parts.

%C a(n) = Sum_{k>=1} k*A116799(n,k). - _Emeric Deutsch_, Feb 24 2006

%H Vaclav Kotesovec, <a href="/A092322/b092322.txt">Table of n, a(n) for n = 1..2500</a>

%F G.f.: Sum_{n>=1} (2*n-1)*x^(2*n-1)/Product_{k=1..n} (1-x^(2*k-1)).

%e a(5)=9 because the partitions of 5 into odd parts are [5],[3,1,1] and [1,1,1,1,1] and the largest parts add up to 5+3+1=9.

%p g:=sum((2*n-1)*x^(2*n-1)/Product(1-x^(2*k-1),k=1..n),n=1..30): gser:=series(g,x=0,50): seq(coeff(gser,x^n),n=1..48); # _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, 1, n}], {n, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Jul 06 2019 *)

%Y Cf. A092314, A092269, A092309, A092321, A092313, A092310, A092311, A092268.

%Y Cf. A116799.

%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