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

55,3

Links

Table of n, a(n) for n=55..103.

Formula

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

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] &

Crossrefs

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

Sequence in context: A218511 A008640 A008634 * A238869 A326333 A036011

Adjacent sequences: A347574 A347575 A347576 * A347578 A347579 A347580

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 07 2021

Status

approved