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A327291 Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size eight are used and the colors are introduced in increasing order.

%I A327291 #7 Sep 18 2019 12:39:18
%S A327291 1,2,5,10,20,36,65,110,185,326,532,879,1417,2272,3563,5572,8543,13031,
%T A327291 19596,29671,43971,65293,95783,140259,203281,294069,421433,602382,
%U A327291 854470,1207812,1700895,2382536,3323738,4619166,6394401,8817059,12117260,16588535,22637178
%N A327291 Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size eight are used and the colors are introduced in increasing order.
%H A327291 Alois P. Heinz, <a href="/A327291/b327291.txt">Table of n, a(n) for n = 36..5000</a>
%F A327291 a(n) ~ exp(sqrt(2*(Pi^2 - 6*polylog(2,-7))*n/3)) * sqrt(Pi^2 - 6*polylog(2,-7)) / (4*8!*sqrt(24)*Pi*n). - _Vaclav Kotesovec_, Sep 18 2019
%p A327291 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A327291      (t-> b(t, min(t, i-1), k))(n-i*j), j=1..n/i)*k+b(n, i-1, k)))
%p A327291     end:
%p A327291 a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k)/k!)(8):
%p A327291 seq(a(n), n=36..75);
%Y A327291 Column k=8 of A321878.
%K A327291 nonn
%O A327291 36,2
%A A327291 _Alois P. Heinz_, Aug 28 2019