A320696 Number of partitions of n with up to nine distinct kinds of 1.

1, 9, 37, 94, 173, 266, 388, 568, 826, 1176, 1641, 2256, 3064, 4115, 5472, 7215, 9437, 12250, 15798, 20253, 25813, 32721, 41277, 51836, 64813, 80700, 100093, 123707, 152370, 187047, 228895, 279284, 339806, 412322, 499014, 602430, 725543, 871815, 1045274

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

a(n) ~ Pi * 2^(13/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - Vaclav Kotesovec, Oct 24 2018

G.f.: (1 + x)^9 * Product_{k>=2} 1 / (1 - x^k). - Ilya Gutkovskiy, Apr 24 2021

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1,
      binomial(9, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..60);

Crossrefs

Column k=9 of A292622.

Sequence in context: A022276 A171443 A341403 * A299290 A304290 A244245

Adjacent sequences: A320693 A320694 A320695 * A320697 A320698 A320699

Keyword

nonn

Author

Alois P. Heinz, Oct 19 2018

Status

approved