cp's OEIS Frontend

A327293 Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size ten are used and the colors are introduced in increasing order.

%I A327293 #8 Sep 18 2019 12:42:14
%S A327293 1,2,5,10,20,36,65,110,185,300,481,795,1250,1982,3087,4798,7332,11191,
%T A327293 16821,25196,37308,54951,80131,117346,169306,244417,349967,500258,
%U A327293 709715,1005550,1414751,1986544,2773496,3861747,5349095,7389698,10178856,13964050,19102030
%N A327293 Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size ten are used and the colors are introduced in increasing order.
%C A327293 In general, for k>=1, is column k of A321878 asymptotic to exp(sqrt(2*(Pi^2 - 6*polylog(2, 1-k))*n/3)) * sqrt(Pi^2 - 6*polylog(2, 1-k)) / (4*k!*sqrt(3*k)*Pi*n). - _Vaclav Kotesovec_, Sep 18 2019
%H A327293 Alois P. Heinz, <a href="/A327293/b327293.txt">Table of n, a(n) for n = 55..5000</a>
%F A327293 a(n) ~ exp(sqrt(2*(Pi^2 - 6*polylog(2,-9))*n/3)) * sqrt(Pi^2 - 6*polylog(2,-9)) / (4*10!*sqrt(30)*Pi*n). - _Vaclav Kotesovec_, Sep 18 2019
%p A327293 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A327293      (t-> b(t, min(t, i-1), k))(n-i*j), j=1..n/i)*k+b(n, i-1, k)))
%p A327293     end:
%p A327293 a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k)/k!)(10):
%p A327293 seq(a(n), n=55..93);
%Y A327293 Column k=10 of A321878.
%K A327293 nonn
%O A327293 55,2
%A A327293 _Alois P. Heinz_, Aug 28 2019