OFFSET
0,3
COMMENTS
Diagonal of array T(n,k) = binomial(kn,n)/(1+(k-1)n).
Number of paths up and left from (0,0) to (n^2-n,n) where x/y <= n-1 for all intermediate points. - Henry Bottomley, Dec 25 2003
Empirical: In the ring of symmetric functions over the fraction field Q(q, t), letting s(1^n) denote the Schur function indexed by (1^n), a(n) is equal to the coefficient of s(n) in nabla^(n)s(1^n) with q=t=1, where nabla denotes the "nabla operator" on symmetric functions, and s(n) denotes the Schur function indexed by the integer partition (n) of n. - John M. Campbell, Apr 06 2018
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), 307-344.
FORMULA
MAPLE
MATHEMATICA
Table[Binomial[n^2, n] / (n (n - 1) + 1), {n, 0, 20}] (* Vincenzo Librandi, Apr 07 2018 *)
PROG
(PARI) a(n) = binomial(n^2, n)/(n*(n-1)+1); \\ Altug Alkan, Apr 06 2018
(Magma) [Binomial(n^2, n)/(1+(n-1)*n): n in [0..20]]; // Vincenzo Librandi, Apr 07 2018
(GAP) List([0..20], n->Binomial(n^2, n)/(1+(n-1)*n)); # Muniru A Asiru, Apr 08 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Dec 22 2003
STATUS
approved