A347575 Number of partitions of n into 8 or more distinct parts.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 54, 73, 94, 123, 157, 201, 252, 318, 394, 489, 600, 735, 892, 1083, 1302, 1564, 1867, 2224, 2634, 3116, 3665, 4305, 5035, 5877, 6834, 7935, 9179, 10601, 12208, 14033, 16087, 18415, 21024, 23968, 27264, 30965, 35097, 39728, 44881

Offset: 36

Author

Ilya Gutkovskiy, Sep 07 2021

Keywords

• nonn

Crossrefs

Cf. A111133, A347548, A347549, A347572, A347573, A347574, A347576, A347577.

Programs

Mathematica

nmax = 85; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 8, nmax}], {x, 0, nmax}], x] // Drop[#, 36] &

Formula

G.f.: Sum_{k>=8} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).