A347572 Number of partitions of n into 5 or more distinct parts.

1, 1, 2, 3, 5, 7, 11, 14, 20, 26, 35, 44, 58, 72, 91, 112, 139, 168, 206, 246, 297, 353, 420, 494, 584, 682, 798, 927, 1077, 1243, 1437, 1649, 1894, 2166, 2475, 2817, 3207, 3636, 4121, 4658, 5261, 5926, 6673, 7494, 8412, 9425, 10550, 11788, 13166, 14677, 16352

Offset

15,3

Links

Table of n, a(n) for n=15..65.

Formula

G.f.: Sum_{k>=5} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).

Mathematica

nmax = 65; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 5, nmax}], {x, 0, nmax}], x] // Drop[#, 15] &

Crossrefs

Cf. A111133, A347548, A347549, A347573, A347574, A347575, A347576, A347577.

Sequence in context: A001402 A377077 A008629 * A363068 A238864 A070289

Adjacent sequences: A347569 A347570 A347571 * A347573 A347574 A347575

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 07 2021

Status

approved