A339222 Number of partitions of n into parts >= 2 where every part appears at least 2 times.

1, 0, 0, 0, 1, 0, 2, 0, 2, 1, 3, 0, 6, 1, 6, 3, 10, 2, 15, 4, 18, 9, 25, 8, 38, 14, 44, 24, 62, 26, 86, 39, 105, 61, 139, 70, 191, 100, 230, 144, 304, 173, 400, 235, 490, 326, 629, 395, 819, 525, 996, 701, 1269, 859, 1617, 1114, 1974, 1456, 2475, 1783, 3124, 2279, 3793, 2920

Offset

0,7

Links

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

Index entries for sequences related to partitions

Formula

G.f.: Product_{k>=2} (1 + x^(2*k) / (1 - x^k)).

a(n) ~ exp(2*Pi*sqrt(n)/3) * Pi / (18*sqrt(2)*n^(3/2)). - Vaclav Kotesovec, Dec 09 2020

Example

a(12) = 6 because we have [6, 6], [4, 4, 4], [4, 4, 2, 2], [3, 3, 3, 3], [3, 3, 2, 2, 2] and [2, 2, 2, 2, 2, 2].

Mathematica

nmax = 63; CoefficientList[Series[Product[1 + x^(2 k)/(1 - x^k), {k, 2, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A002865, A007690.

Sequence in context: A349438 A078152 A339242 * A191247 A308263 A028932

Adjacent sequences: A339219 A339220 A339221 * A339223 A339224 A339225

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 27 2020

Status

approved