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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.
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%I #8 Sep 18 2019 12:42:14

%S 1,2,5,10,20,36,65,110,185,300,481,795,1250,1982,3087,4798,7332,11191,

%T 16821,25196,37308,54951,80131,117346,169306,244417,349967,500258,

%U 709715,1005550,1414751,1986544,2773496,3861747,5349095,7389698,10178856,13964050,19102030

%N 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 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 Alois P. Heinz, <a href="/A327293/b327293.txt">Table of n, a(n) for n = 55..5000</a>

%F 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 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(

%p (t-> b(t, min(t, i-1), k))(n-i*j), j=1..n/i)*k+b(n, i-1, k)))

%p end:

%p a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k)/k!)(10):

%p seq(a(n), n=55..93);

%Y Column k=10 of A321878.

%K nonn

%O 55,2

%A _Alois P. Heinz_, Aug 28 2019