%I #6 Oct 25 2018 04:10:20

%S 1,29,492,6401,70880,704676,6490951,56524414,471750268,3810085913,

%T 29989229889,231255237342,1754111872952,13128442914265,97189645391839,

%U 713050007293418,5192646586543845,37581376345173772,270593146238709314,1939929376873532436

%N 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 Alois P. Heinz, <a href="/A320550/b320550.txt">Table of n, a(n) for n = 8..1000</a>

%F a(n) ~ 7^(n-1) / (7! * QPochhammer[1/7]). - _Vaclav Kotesovec_, Oct 25 2018

%p b:= proc(n, i, k) option remember; `if`(n=0 or i=1, k^(n-1),

%p b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k)))

%p end:

%p A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, k*b(n$2, k-1))):

%p a:= n-> (k-> add(A(n, k-i)*(-1)^i/(i!*(k-i)!), i=0..k))(8):

%p seq(a(n), n=8..40);

%Y Column k=8 of A262495.

%Y Cf. A258463.

%K nonn

%O 8,2

%A _Alois P. Heinz_, Oct 15 2018