A347577 Number of partitions of n into 10 or more distinct parts.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 76, 99, 131, 169, 219, 278, 355, 445, 560, 695, 863, 1061, 1304, 1588, 1933, 2336, 2819, 3381, 4050, 4824, 5738, 6793, 8028, 9450, 11105, 13000, 15195, 17702, 20588, 23874, 27640, 31913, 36790, 42308, 48578, 55654, 63666

Offset: 55

Author

Ilya Gutkovskiy, Sep 07 2021

Keywords

• nonn

Crossrefs

Cf. A111133, A347548, A347549, A347572, A347573, A347574, A347575, A347576.

Programs

Mathematica

nmax = 103; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 10, nmax}], {x, 0, nmax}], x] // Drop[#, 55] &

Formula

G.f.: Sum_{k>=10} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).