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

15,1

Links

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

Formula

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

Maple

b:= proc(n, i, t) option remember; `if`(t>i or t*(t+1)/2>n
      or 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))))
    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 *)

Crossrefs

Column k=5 of A131632.

Sequence in context: A034645 A204054 A206196 * A246232 A248710 A376794

Adjacent sequences: A272514 A272515 A272516 * A272518 A272519 A272520

Keyword

nonn

Author

Alois P. Heinz, May 01 2016

Status

approved