OFFSET
0,4
COMMENTS
For n>=1 the number of standard Young tableaux with shapes corresponding to partitions into two distinct parts. - Joerg Arndt, Oct 25 2012
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = A037952(n) - 1. Proof by Ira Gessel: Write down the number of such subsets with k elements <= (n-1)/2 as a product of two binomial coefficients, then evaluate the sum using Vandermonde's theorem.
MAPLE
a:= n-> binomial(n, iquo(n-1, 2))-1:
seq(a(n), n=0..40); # Alois P. Heinz, Nov 17 2012
MATHEMATICA
a[n_] := Binomial[n, Floor[(n-1)/2]]-1; a[0] = 0; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jul 03 2015 *)
PROG
(Magma) [0] cat [Binomial(n, Floor((n-1)/2))-1: n in [1..40]]; // Vincenzo Librandi, Jul 03 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved