A272519 Number of set partitions of [n] into seven blocks with distinct sizes.

2431106898187968000, 8812762505931384000, 67144857188048640000, 416298114565901568000, 3144312274410635328000, 23728992530256389376000, 238675412699786289427200, 3207620559498676985664000, 16207982672116390803648000, 117220515926387332979520000

Offset: 28

Author

Alois P. Heinz, May 01 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 28..1000

Crossrefs

Column k=7 of A131632.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(t>i or t*(t+1)/2>n
      or t*(2*i+1-t)/2n, 0, b(n-i, i-1, t-1)*binomial(n,i))))
    end:
a:= n-> b(n$2, 7):
seq(a(n), n=28..40);

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[t > i || t*(t + 1)/2 > n || t*(2*i + 1 - t)/2 < n, 0, If[n == 0, 1, b[n, i - 1, t] + If[i > n, 0, b[n - i, i - 1, t - 1]*Binomial[n, i]]]];
a[n_] := b[n, n, 7];
Table[a[n], {n, 28, 40}] (* Jean-François Alcover, May 24 2018, translated from Maple *)

Formula

a(n) = n! * [x^n*y^7] Product_{n>=1} (1+y*x^n/n!).