A320693 - OEIS

%I #10 Apr 24 2021 20:44:19

%S 1,6,16,27,38,55,82,119,168,233,319,432,578,766,1008,1315,1702,2191,

%T 2804,3566,4512,5683,7126,8897,11061,13700,16913,20807,25510,31183,

%U 38009,46198,56002,67713,81671,98276,117989,141349,168984,201609,240058,285310,338480

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

%H Alois P. Heinz, <a href="/A320693/b320693.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ Pi * 2^(7/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - _Vaclav Kotesovec_, Oct 24 2018

%F G.f.: (1 + x)^6 * Product_{k>=2} 1 / (1 - x^k). - _Ilya Gutkovskiy_, Apr 24 2021

%p b:= proc(n, i) option remember; `if`(n=0 or i=1,

%p       binomial(6, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))

%p     end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..60);

%Y Column k=6 of A292622.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 19 2018