A320549 - OEIS

%I #6 Oct 25 2018 04:10:00

%S 1,22,289,2957,26073,208516,1558219,11087757,76079369,507834036,

%T 3318628468,21330628088,135325211035,849659803048,5290544985029,

%U 32722489543068,201296535411532,1232850239281547,7523511821702402,45777353201698899,277862479922939524

%N Number of partitions of n into parts of exactly seven sorts which are introduced in ascending order such that sorts of adjacent parts are different.

%H Alois P. Heinz, <a href="/A320549/b320549.txt">Table of n, a(n) for n = 7..1000</a>

%F a(n) ~ 6^(n-1) / (6! * QPochhammer[1/6]). - _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))(7):

%p seq(a(n), n=7..40);

%Y Column k=7 of A262495.

%Y Cf. A258462.

%K nonn

%O 7,2

%A _Alois P. Heinz_, Oct 15 2018