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A268347 Number of partitions of (4, n) into a sum of distinct pairs. 3

%I

%S 2,7,14,27,46,74,116,174,254,363,510,703,957,1285,1706,2244,2924,3777,

%T 4844,6168,7802,9813,12272,15267,18902,23295,28584,34935,42532,51592,

%U 62369,75150,90265,108102,129094,153743,182627,216395,255792,301672,354994,416851

%N Number of partitions of (4, n) into a sum of distinct pairs.

%H Vaclav Kotesovec, <a href="/A268347/b268347.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ 3^(3/4) * n^(5/4) * exp(Pi*sqrt(n/3)) / (2*Pi^4).

%t max=50; col=4; 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-Fran├žois Alcover_ *)

%t nmax = 50; CoefficientList[Series[((2 + 3*x - x^3 - 4*x^4 - 2*x^5 + x^6 + x^7 + 2*x^8 - x^9) / ((1 - x)*(1 - x^2)*(1 - x^3)*(1 - x^4)))*Product[1 + x^k, {k, 1, nmax}], {x, 0, nmax}], x]

%Y Column 4 of A054242.

%K nonn

%O 0,1

%A _Vaclav Kotesovec_, Feb 02 2016

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Last modified January 17 19:55 EST 2022. Contains 350406 sequences. (Running on oeis4.)