A320693 Number of partitions of n with up to six distinct kinds of 1.

1, 6, 16, 27, 38, 55, 82, 119, 168, 233, 319, 432, 578, 766, 1008, 1315, 1702, 2191, 2804, 3566, 4512, 5683, 7126, 8897, 11061, 13700, 16913, 20807, 25510, 31183, 38009, 46198, 56002, 67713, 81671, 98276, 117989, 141349, 168984, 201609, 240058, 285310, 338480

Offset

0,2

Links

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

Formula

a(n) ~ Pi * 2^(7/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - Vaclav Kotesovec, Oct 24 2018

G.f.: (1 + x)^6 * 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(6, 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=6 of A292622.

Sequence in context: A212905 A191117 A265389 * A274848 A201020 A088818

Adjacent sequences: A320690 A320691 A320692 * A320694 A320695 A320696

Keyword

nonn

Author

Alois P. Heinz, Oct 19 2018

Status

approved