A268345 - OEIS

%I #7 Feb 04 2016 14:14:23

%S 1,3,5,9,14,21,31,44,61,83,112,148,194,251,322,410,518,649,809,1002,

%T 1234,1513,1846,2242,2712,3268,3923,4694,5598,6655,7889,9326,10994,

%U 12929,15167,17751,20730,24157,28092,32605,37771,43675,50414,58094,66833,76767

%N Number of partitions of (2, n) into a sum of distinct pairs.

%H Vaclav Kotesovec, <a href="/A268345/b268345.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ 3^(3/4) * n^(1/4) * exp(Pi*sqrt(n/3)) / (2*Pi^2).

%t max=50; col=2; 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[(1 + x - x^2)/((1 - x)*(1 - x^2)) * Product[1 + x^k, {k, 1, nmax}], {x, 0, nmax}], x]

%Y Column 2 of A054242.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Feb 02 2016