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

36,3

Links

Table of n, a(n) for n=36..85.

Formula

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

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] &

Crossrefs

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

Sequence in context: A341913 A008638 A008632 * A238867 A035988 A088669

Adjacent sequences: A347572 A347573 A347574 * A347576 A347577 A347578

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 07 2021

Status

approved