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.

1, 29, 492, 6401, 70880, 704676, 6490951, 56524414, 471750268, 3810085913, 29989229889, 231255237342, 1754111872952, 13128442914265, 97189645391839, 713050007293418, 5192646586543845, 37581376345173772, 270593146238709314, 1939929376873532436

Offset: 8

Author

Alois P. Heinz, Oct 15 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..1000

Crossrefs

Column k=8 of A262495.

Cf. A258463.

Programs

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))(8):
seq(a(n), n=8..40);

Formula

a(n) ~ 7^(n-1) / (7! * QPochhammer[1/7]). - Vaclav Kotesovec, Oct 25 2018