A272516 Number of set partitions of [n] into four blocks with distinct sizes.

12600, 27720, 138600, 643500, 4408404, 12687675, 60780720, 238299880, 1295666424, 4208874756, 18840460800, 72351683460, 361100656224, 1228553894491, 5370616442928, 20605640103400, 97659853077800, 342942099783075, 1479570975628200, 5678915129142255

Offset

10,1

Links

Alois P. Heinz, Table of n, a(n) for n = 10..1000

Formula

a(n) = n! * [x^n*y^4] 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, 4):
seq(a(n), n=10..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, 4];
a /@ Range[10, 40] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

Crossrefs

Column k=4 of A131632.

Sequence in context: A216990 A237086 A190109 * A246231 A248709 A352586

Adjacent sequences: A272513 A272514 A272515 * A272517 A272518 A272519

Keyword

nonn

Author

Alois P. Heinz, May 01 2016

Status

approved