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

2, 7, 14, 27, 46, 74, 116, 174, 254, 363, 510, 703, 957, 1285, 1706, 2244, 2924, 3777, 4844, 6168, 7802, 9813, 12272, 15267, 18902, 23295, 28584, 34935, 42532, 51592, 62369, 75150, 90265, 108102, 129094, 153743, 182627, 216395, 255792, 301672, 354994, 416851

Offset

0,1

Links

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

Formula

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

Mathematica

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-François Alcover *)
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]

Crossrefs

Column 4 of A054242.

Sequence in context: A333644 A014112 A227016 * A210728 A294533 A294541

Adjacent sequences: A268344 A268345 A268346 * A268348 A268349 A268350

Keyword

nonn

Author

Vaclav Kotesovec, Feb 02 2016

Status

approved