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A327289 Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size six are used and the colors are introduced in increasing order.

%I A327289 #7 Sep 18 2019 12:38:37
%S A327289 1,2,5,10,20,36,65,123,210,362,603,994,1595,2541,3956,6225,9501,14516,
%T A327289 21820,32703,48315,71175,103589,150167,216413,309627,440400,623404,
%U A327289 877303,1228493,1712235,2374639,3278894,4507571,6175713,8421243,11447049,15496728
%N A327289 Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size six are used and the colors are introduced in increasing order.
%H A327289 Alois P. Heinz, <a href="/A327289/b327289.txt">Table of n, a(n) for n = 21..5000</a>
%F A327289 a(n) ~ exp(sqrt(2*(Pi^2 - 6*polylog(2,-5))*n/3)) * sqrt(Pi^2 - 6*polylog(2,-5)) / (4*6!*sqrt(18)*Pi*n). - _Vaclav Kotesovec_, Sep 18 2019
%p A327289 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A327289      (t-> b(t, min(t, i-1), k))(n-i*j), j=1..n/i)*k+b(n, i-1, k)))
%p A327289     end:
%p A327289 a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k)/k!)(6):
%p A327289 seq(a(n), n=21..59);
%Y A327289 Column k=6 of A321878.
%K A327289 nonn
%O A327289 21,2
%A A327289 _Alois P. Heinz_, Aug 28 2019