OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..198
FORMULA
a(n) = A241981(2n,n).
a(n) ~ 2^(3*n+1/2) * n^(2*n-1) / exp(n). - Vaclav Kotesovec, Aug 19 2014
EXAMPLE
a(1) = 3: (1,1), (1,2), (2,2).
MAPLE
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
b(n-i*j, i-1), j=0..n/i)))
end:
A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, min(j, k)), j=0..n):
a:= n-> `if`(n=0, 1, A(2*n, n) -A(2*n, n-1)):
seq(a(n), n=0..15);
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_] := b[n, i] = Which[n==0, 1, i<1, 0, True, Sum[(i-1)!^j* multinomial[n, Join[{n-i*j}, Table[i, {j}]]]/j!*b[n-i*j, i-1], {j, 0, n/i} ] ];
A[n_, k_] := Sum[Binomial[n-1, j-1]*n^(n-j)*b[j, Min[j, k]], {j, 0, n}];
a[n_] := If[n == 0, 1, A[2n, n] - A[2n, n-1]];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Apr 01 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 10 2014
STATUS
approved