OFFSET
1,1
COMMENTS
a(n) is odd if and only if n = 3 or n in { 2^k-3, 2^k-1 : k = 3,4,5, ... }.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012.
G. Kreweras, Sur les extensions lineaires d'une famille particuliere d'ordres partiels, Discrete Math., 27 (1979), 279-295.
G. Kreweras, Sur les extensions linéaires d'une famille particulière d'ordres partiels, Discrete Math., 27 (1979), 279-295. (Annotated scanned copy)
Wikipedia, Young tableau
FORMULA
a(n) = 2*(2*n+1)*(n^2+5*n+2)*n/((n-1)*(n+3)*(n^2+3*n-2))*a(n-1); a(1) = 2.
MAPLE
a:= proc(n) option remember; `if`(n=1, 2,
(4+(18+(22+4*n)*n)*n)*n*a(n-1)/(6+(-13+(1+(5+n)*n)*n)*n))
end:
seq(a(n), n=1..30);
MATHEMATICA
a[1] = 2; a[n_] := a[n] = (4 + (18 + (22 + 4*n)*n)*n)*n*a[n - 1]/(6 + (-13 + (1 + (5 + n)*n)*n)*n); Array[a, 30] (* Jean-François Alcover, Nov 08 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 28 2012
STATUS
approved