A268345 Number of partitions of (2, n) into a sum of distinct pairs.

1, 3, 5, 9, 14, 21, 31, 44, 61, 83, 112, 148, 194, 251, 322, 410, 518, 649, 809, 1002, 1234, 1513, 1846, 2242, 2712, 3268, 3923, 4694, 5598, 6655, 7889, 9326, 10994, 12929, 15167, 17751, 20730, 24157, 28092, 32605, 37771, 43675, 50414, 58094, 66833, 76767

Offset

0,2

Links

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

Formula

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

Mathematica

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 *)
nmax = 50; CoefficientList[Series[(1 + x - x^2)/((1 - x)*(1 - x^2)) * Product[1 + x^k, {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Column 2 of A054242.

Sequence in context: A310040 A215369 A053618 * A357388 A267047 A032801

Adjacent sequences: A268342 A268343 A268344 * A268346 A268347 A268348

Keyword

nonn

Author

Vaclav Kotesovec, Feb 02 2016

Status

approved