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A327292 Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size nine are used and the colors are introduced in increasing order.

%I A327292 #7 Sep 18 2019 12:39:43
%S A327292 1,2,5,10,20,36,65,110,185,300,515,819,1332,2102,3327,5142,7958,12071,
%T A327292 18271,27256,40462,60036,87981,128502,186484,269466,386757,553271,
%U A327292 786299,1113510,1568109,2199730,3069546,4278447,5924730,8188867,11266659,15464516,21134748
%N A327292 Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size nine are used and the colors are introduced in increasing order.
%H A327292 Alois P. Heinz, <a href="/A327292/b327292.txt">Table of n, a(n) for n = 45..5000</a>
%F A327292 a(n) ~ exp(sqrt(2*(Pi^2 - 6*polylog(2,-8))*n/3)) * sqrt(Pi^2 - 6*polylog(2,-8)) / (4*9!*sqrt(27)*Pi*n). - _Vaclav Kotesovec_, Sep 18 2019
%p A327292 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A327292      (t-> b(t, min(t, i-1), k))(n-i*j), j=1..n/i)*k+b(n, i-1, k)))
%p A327292     end:
%p A327292 a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k)/k!)(9):
%p A327292 seq(a(n), n=45..83);
%Y A327292 Column k=9 of A321878.
%K A327292 nonn
%O A327292 45,2
%A A327292 _Alois P. Heinz_, Aug 28 2019