cp's OEIS Frontend

A320548 Number of partitions of n into parts of exactly six sorts which are introduced in ascending order such that sorts of adjacent parts are different.

%I A320548 #6 Oct 25 2018 04:09:39
%S A320548 1,16,157,1223,8331,52078,307123,1738442,9552826,51357799,271624228,
%T A320548 1418856967,7341442171,37708533544,192586163135,979219603193,
%U A320548 4961598120154,25071026570558,126410385741982,636282269651863,3198360710675384,16059685006324807
%N A320548 Number of partitions of n into parts of exactly six sorts which are introduced in ascending order such that sorts of adjacent parts are different.
%H A320548 Alois P. Heinz, <a href="/A320548/b320548.txt">Table of n, a(n) for n = 6..1000</a>
%F A320548 a(n) ~ 5^(n-1) / (5! * QPochhammer[1/5]). - _Vaclav Kotesovec_, Oct 25 2018
%p A320548 b:= proc(n, i, k) option remember; `if`(n=0 or i=1, k^(n-1),
%p A320548       b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k)))
%p A320548     end:
%p A320548 A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, k*b(n$2, k-1))):
%p A320548 a:= n-> (k-> add(A(n, k-i)*(-1)^i/(i!*(k-i)!), i=0..k))(6):
%p A320548 seq(a(n), n=6..40);
%Y A320548 Column k=6 of A262495.
%Y A320548 Cf. A258461.
%K A320548 nonn
%O A320548 6,2
%A A320548 _Alois P. Heinz_, Oct 15 2018