cp's OEIS Frontend

A327290 Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size seven are used and the colors are introduced in increasing order.

%I A327290 #7 Sep 18 2019 12:38:56
%S A327290 1,2,5,10,20,36,65,110,204,337,573,934,1527,2416,3826,5907,9088,13963,
%T A327290 21070,31642,47131,69707,102214,149143,215754,310547,443840,633139,
%U A327290 895294,1262971,1770236,2473601,3436809,4761393,6561269,9015761,12330231,16812326
%N A327290 Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size seven are used and the colors are introduced in increasing order.
%H A327290 Alois P. Heinz, <a href="/A327290/b327290.txt">Table of n, a(n) for n = 28..5000</a>
%F A327290 a(n) ~ exp(sqrt(2*(Pi^2 - 6*polylog(2,-6))*n/3)) * sqrt(Pi^2 - 6*polylog(2,-6)) / (4*7!*sqrt(21)*Pi*n). - _Vaclav Kotesovec_, Sep 18 2019
%p A327290 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A327290      (t-> b(t, min(t, i-1), k))(n-i*j), j=1..n/i)*k+b(n, i-1, k)))
%p A327290     end:
%p A327290 a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k)/k!)(7):
%p A327290 seq(a(n), n=28..65);
%Y A327290 Column k=7 of A321878.
%K A327290 nonn
%O A327290 28,2
%A A327290 _Alois P. Heinz_, Aug 28 2019