A347576 Number of partitions of n into 9 or more distinct parts.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 55, 75, 97, 128, 164, 212, 267, 340, 423, 530, 654, 808, 986, 1207, 1460, 1768, 2123, 2549, 3037, 3620, 4284, 5069, 5965, 7012, 8203, 9590, 11160, 12975, 15029, 17388, 20048, 23092, 26513, 30408, 34781, 39734, 45278

Offset

45,3

Links

Table of n, a(n) for n=45..92.

Formula

G.f.: Sum_{k>=9} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).

Mathematica

nmax = 92; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 9, nmax}], {x, 0, nmax}], x] // Drop[#, 45] &

Crossrefs

Cf. A111133, A347548, A347549, A347572, A347573, A347574, A347575, A347577.

Sequence in context: A008639 A341914 A008633 * A238868 A035999 A036010

Adjacent sequences: A347573 A347574 A347575 * A347577 A347578 A347579

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 07 2021

Status

approved