A320694 Number of partitions of n with up to seven distinct kinds of 1.

1, 7, 22, 43, 65, 93, 137, 201, 287, 401, 552, 751, 1010, 1344, 1774, 2323, 3017, 3893, 4995, 6370, 8078, 10195, 12809, 16023, 19958, 24761, 30613, 37720, 46317, 56693, 69192, 84207, 102200, 123715, 149384, 179947, 216265, 259338, 310333, 370593, 441667

Offset

0,2

Links

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

Formula

a(n) ~ Pi * 2^(9/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - Vaclav Kotesovec, Oct 24 2018

G.f.: (1 + x)^7 * 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(7, 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=7 of A292622.

Sequence in context: A275642 A171441 A341401 * A261465 A033954 A159227

Adjacent sequences: A320691 A320692 A320693 * A320695 A320696 A320697

Keyword

nonn

Author

Alois P. Heinz, Oct 19 2018

Status

approved