A272514 Number of set partitions of [n] into two blocks with distinct sizes.

3, 4, 15, 21, 63, 92, 255, 385, 1023, 1585, 4095, 6475, 16383, 26332, 65535, 106761, 262143, 431909, 1048575, 1744435, 4194303, 7036529, 16777215, 28354131, 67108863, 114159427, 268435455, 459312151, 1073741823, 1846943452, 4294967295, 7423131481, 17179869183

Offset

3,1

Links

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Formula

a(n) = n! * [x^n*y^2] Product_{n>=1} (1+y*x^n/n!).

a(n) = Sum_{i=1..floor((n-1)/2)} binomial(n,i). - Wesley Ivan Hurt, Nov 15 2017

a(n) ~ 2^(n-1). - Vaclav Kotesovec, Dec 11 2020

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, 2):
seq(a(n), n=3..40);

Mathematica

Table[Sum[Binomial[n, i], {i, Floor[(n - 1)/2]}], {n, 3, 35}] (* Michael De Vlieger, Nov 15 2017 *)

Crossrefs

Column k=2 of A131632.

Sequence in context: A369910 A095799 A109926 * A065942 A369082 A036759

Adjacent sequences: A272511 A272512 A272513 * A272515 A272516 A272517

Keyword

nonn,easy

Author

Alois P. Heinz, May 01 2016

Status

approved