A268346 - OEIS

%I #6 Feb 04 2016 14:14:45

%S 2,5,9,17,27,42,64,93,132,185,254,343,459,605,790,1024,1314,1673,2118,

%T 2661,3324,4132,5107,6282,7695,9383,11396,13792,16629,19982,23938,

%U 28586,34037,40420,47868,56546,66640,78348,91908,107589,125680,146522,170499,198027

%N Number of partitions of (3, n) into a sum of distinct pairs.

%H Vaclav Kotesovec, <a href="/A268346/b268346.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ 3^(1/4) * n^(3/4) * exp(Pi*sqrt(n/3)) / Pi^3.

%t max=50; col=3; s1=Series[Product[(1+x^(n-k)*y^k), {n, 1, max+2}, {k, 0, n}], {y, 0, col}]//Normal; s2=Series[s1, {x, 0, max+1}]; a[n_]:=SeriesCoefficient[s2, {x, 0, n}, {y, 0, col}]; Table[a[n], {n, 0, max}] (* after _Jean-François Alcover_ *)

%t nmax = 50; CoefficientList[Series[((2 + x - x^2 - x^3 - x^4 + x^5) / ((1 - x)*(1 - x^2)*(1 - x^3))) * Product[1 + x^k, {k, 1, nmax}], {x, 0, nmax}], x]

%Y Column 3 of A054242.

%K nonn

%O 0,1

%A _Vaclav Kotesovec_, Feb 02 2016