A385408 Sum over all ordered partitions of [n] of 6^j for an ordered partition with j inversions.

1, 1, 8, 388, 113480, 199246816, 2099255895008, 132708276995157568, 50336523318422432038400, 114556539064849604787867141376, 1564256035642651626332994903500876288, 128158392280785912677966097933268099449960448, 62999559569114394473388668602373642996554916532377600

Offset: 0

Author

Alois P. Heinz, Jun 27 2025

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..51
• Wikipedia, Inversion
• Wikipedia, Partition of a set

Crossrefs

Column k=6 of A381426.

Cf. A000670, A381299.

Programs

Maple

b:= proc(o, u, t) option remember; `if`(u+o=0, 1, `if`(t=1,
      b(u+o, 0$2), 0)+add(6^(u+j-1)*b(o-j, u+j-1, 1), j=1..o))
    end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..14);

Formula

a(n) = Sum_{k=0..binomial(n,2)} A381299(n,k)*6^k.