cp's OEIS Frontend

A320552 Number of partitions of n into parts of exactly ten sorts which are introduced in ascending order such that sorts of adjacent parts are different.

%I A320552 #6 Oct 25 2018 04:11:12
%S A320552 1,46,1202,23523,384227,5542879,73055550,899381476,10501235760,
%T A320552 117575627562,1272685923725,13401470756234,137945728220808,
%U A320552 1393299928219652,13851195993229478,135865787060384468,1317624915100586227,12654868264707472392,120534359759023933905
%N A320552 Number of partitions of n into parts of exactly ten sorts which are introduced in ascending order such that sorts of adjacent parts are different.
%H A320552 Alois P. Heinz, <a href="/A320552/b320552.txt">Table of n, a(n) for n = 10..1000</a>
%F A320552 a(n) ~ 9^(n-1) / (9! * QPochhammer[1/9]). - _Vaclav Kotesovec_, Oct 25 2018
%p A320552 b:= proc(n, i, k) option remember; `if`(n=0 or i=1, k^(n-1),
%p A320552       b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k)))
%p A320552     end:
%p A320552 A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, k*b(n$2, k-1))):
%p A320552 a:= n-> (k-> add(A(n, k-i)*(-1)^i/(i!*(k-i)!), i=0..k))(10):
%p A320552 seq(a(n), n=10..40);
%Y A320552 Column k=10 of A262495.
%Y A320552 Cf. A258465.
%K A320552 nonn
%O A320552 10,2
%A A320552 _Alois P. Heinz_, Oct 15 2018