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Number of partitions of (5, n) into a sum of distinct pairs.
3

%I #6 Feb 04 2016 14:15:33

%S 3,10,21,42,74,123,197,303,452,659,943,1323,1830,2496,3363,4485,5922,

%T 7748,10058,12958,16578,21077,26637,33476,41855,52077,64496,79536,

%U 97683,119505,145671,176948,214225,258542,311085,373227,446553,532873,634265,753118

%N Number of partitions of (5, n) into a sum of distinct pairs.

%H Vaclav Kotesovec, <a href="/A268348/b268348.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ 3^(5/4) * n^(7/4) * exp(Pi*sqrt(n/3)) / (5*Pi^5).

%t max=50; col=5; 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[((3 + 4*x + x^2 - 4*x^4 - 5*x^5 - 4*x^6 + 2*x^8 + 3*x^9 + 3*x^10 - x^12 - 2*x^13 + x^14) / ((1 - x)*(1 - x^2)*(1 - x^3)*(1 - x^4)*(1 - x^5)))*Product[1 + x^k, {k, 1, nmax}], {x, 0, nmax}], x]

%Y Column 5 of A054242.

%K nonn

%O 0,1

%A _Vaclav Kotesovec_, Feb 02 2016