A347574 Number of partitions of n into 7 or more distinct parts.

1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 52, 70, 89, 116, 146, 186, 231, 289, 354, 437, 530, 645, 775, 934, 1112, 1327, 1569, 1856, 2179, 2559, 2985, 3483, 4040, 4684, 5406, 6235, 7160, 8218, 9396, 10735, 12225, 13910, 15780, 17888, 20223, 22842, 25742, 28983, 32562

Offset

28,3

Links

Chai Wah Wu, Table of n, a(n) for n = 28..10000

Formula

G.f.: Sum_{k>=7} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).

Mathematica

nmax = 77; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 7, nmax}], {x, 0, nmax}], x] // Drop[#, 28] &

Crossrefs

Cf. A111133, A347548, A347549, A347572, A347573, A347575, A347576, A347577.

Sequence in context: A026814 A008637 A008631 * A238866 A035978 A319475

Adjacent sequences: A347571 A347572 A347573 * A347575 A347576 A347577

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 07 2021

Status

approved