cp's OEIS Frontend

A320550 Number of partitions of n into parts of exactly eight sorts which are introduced in ascending order such that sorts of adjacent parts are different.

%I A320550 #6 Oct 25 2018 04:10:20
%S A320550 1,29,492,6401,70880,704676,6490951,56524414,471750268,3810085913,
%T A320550 29989229889,231255237342,1754111872952,13128442914265,97189645391839,
%U A320550 713050007293418,5192646586543845,37581376345173772,270593146238709314,1939929376873532436
%N A320550 Number of partitions of n into parts of exactly eight sorts which are introduced in ascending order such that sorts of adjacent parts are different.
%H A320550 Alois P. Heinz, <a href="/A320550/b320550.txt">Table of n, a(n) for n = 8..1000</a>
%F A320550 a(n) ~ 7^(n-1) / (7! * QPochhammer[1/7]). - _Vaclav Kotesovec_, Oct 25 2018
%p A320550 b:= proc(n, i, k) option remember; `if`(n=0 or i=1, k^(n-1),
%p A320550       b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k)))
%p A320550     end:
%p A320550 A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, k*b(n$2, k-1))):
%p A320550 a:= n-> (k-> add(A(n, k-i)*(-1)^i/(i!*(k-i)!), i=0..k))(8):
%p A320550 seq(a(n), n=8..40);
%Y A320550 Column k=8 of A262495.
%Y A320550 Cf. A258463.
%K A320550 nonn
%O A320550 8,2
%A A320550 _Alois P. Heinz_, Oct 15 2018