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

%I A320693 #10 Apr 24 2021 20:44:19
%S A320693 1,6,16,27,38,55,82,119,168,233,319,432,578,766,1008,1315,1702,2191,
%T A320693 2804,3566,4512,5683,7126,8897,11061,13700,16913,20807,25510,31183,
%U A320693 38009,46198,56002,67713,81671,98276,117989,141349,168984,201609,240058,285310,338480
%N A320693 Number of partitions of n with up to six distinct kinds of 1.
%H A320693 Alois P. Heinz, <a href="/A320693/b320693.txt">Table of n, a(n) for n = 0..10000</a>
%F A320693 a(n) ~ Pi * 2^(7/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - _Vaclav Kotesovec_, Oct 24 2018
%F A320693 G.f.: (1 + x)^6 * Product_{k>=2} 1 / (1 - x^k). - _Ilya Gutkovskiy_, Apr 24 2021
%p A320693 b:= proc(n, i) option remember; `if`(n=0 or i=1,
%p A320693       binomial(6, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
%p A320693     end:
%p A320693 a:= n-> b(n$2):
%p A320693 seq(a(n), n=0..60);
%Y A320693 Column k=6 of A292622.
%K A320693 nonn
%O A320693 0,2
%A A320693 _Alois P. Heinz_, Oct 19 2018