A272517 Number of set partitions of [n] into five blocks with distinct sizes.

37837800, 100900800, 588107520, 2977294320, 20020160160, 164118754800, 635661248040, 3295178686800, 17741374681800, 95826446465904, 623399389674600, 2664090278249400, 13876038856379700, 71797074694745400, 375274098870636420, 2199911433079733100

Offset: 15

Author

Alois P. Heinz, May 01 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 15..1000

Crossrefs

Column k=5 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, 5):
seq(a(n), n=15..40);

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[t > i || t(t+1)/2 > n || t(2i+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, 5];
a /@ Range[15, 40] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

Formula

a(n) = n! * [x^n*y^5] Product_{n>=1} (1+y*x^n/n!).