A320549 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.

1, 22, 289, 2957, 26073, 208516, 1558219, 11087757, 76079369, 507834036, 3318628468, 21330628088, 135325211035, 849659803048, 5290544985029, 32722489543068, 201296535411532, 1232850239281547, 7523511821702402, 45777353201698899, 277862479922939524

Offset

7,2

Links

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Formula

a(n) ~ 6^(n-1) / (6! * QPochhammer[1/6]). - Vaclav Kotesovec, Oct 25 2018

Maple

b:= proc(n, i, k) option remember; `if`(n=0 or i=1, k^(n-1),
      b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k)))
    end:
A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, k*b(n$2, k-1))):
a:= n-> (k-> add(A(n, k-i)*(-1)^i/(i!*(k-i)!), i=0..k))(7):
seq(a(n), n=7..40);

Crossrefs

Column k=7 of A262495.

Cf. A258462.

Sequence in context: A121792 A020922 A258461 * A211832 A211559 A333063

Adjacent sequences: A320546 A320547 A320548 * A320550 A320551 A320552

Keyword

nonn

Author

Alois P. Heinz, Oct 15 2018

Status

approved