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 A272514 Number of set partitions of [n] into two blocks with distinct sizes. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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)/2n, 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: A041819 A095799 A109926 * A065942 A036759 A263718 Adjacent sequences:  A272511 A272512 A272513 * A272515 A272516 A272517 KEYWORD nonn,easy AUTHOR Alois P. Heinz, May 01 2016 STATUS approved

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Last modified June 12 19:06 EDT 2021. Contains 344959 sequences. (Running on oeis4.)