A268348 Number of partitions of (5, n) into a sum of distinct pairs.

3, 10, 21, 42, 74, 123, 197, 303, 452, 659, 943, 1323, 1830, 2496, 3363, 4485, 5922, 7748, 10058, 12958, 16578, 21077, 26637, 33476, 41855, 52077, 64496, 79536, 97683, 119505, 145671, 176948, 214225, 258542, 311085, 373227, 446553, 532873, 634265, 753118

Offset: 0

Author

Vaclav Kotesovec, Feb 02 2016

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Column 5 of A054242.

Programs

Mathematica

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 *)
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]

Formula

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