cp's OEIS Frontend

A320551 Number of partitions of n into parts of exactly nine sorts which are introduced in ascending order such that sorts of adjacent parts are different.

%I A320551 #6 Oct 25 2018 04:10:45
%S A320551 1,37,788,12705,172520,2084836,23169639,241881526,2406802476,
%T A320551 23064505722,214505275666,1947297442708,17332491414655,
%U A320551 151788374232332,1311496639251360,11205023121317869,94832831557101194,796244028802170279,6640545376656272033
%N A320551 Number of partitions of n into parts of exactly nine sorts which are introduced in ascending order such that sorts of adjacent parts are different.
%H A320551 Alois P. Heinz, <a href="/A320551/b320551.txt">Table of n, a(n) for n = 9..1000</a>
%F A320551 a(n) ~ 8^(n-1) / (8! * QPochhammer[1/8]). - _Vaclav Kotesovec_, Oct 25 2018
%p A320551 b:= proc(n, i, k) option remember; `if`(n=0 or i=1, k^(n-1),
%p A320551       b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k)))
%p A320551     end:
%p A320551 A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, k*b(n$2, k-1))):
%p A320551 a:= n-> (k-> add(A(n, k-i)*(-1)^i/(i!*(k-i)!), i=0..k))(9):
%p A320551 seq(a(n), n=9..40);
%Y A320551 Column k=9 of A262495.
%Y A320551 Cf. A258464.
%K A320551 nonn
%O A320551 9,2
%A A320551 _Alois P. Heinz_, Oct 15 2018