OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
a(n) = A215771(2n,n).
a(n) ~ c * d^n * (n-1)!, where d = 8.52944416851968239902405793921886268..., c = 0.1101477123991489575407024889... . - Vaclav Kotesovec, May 01 2015
MAPLE
b:= proc(n, k) option remember; `if`(k<0 or k>n, 0, `if`(n=0, 1,
add(binomial(n-1, i)*b(n-1-i, k-1)*ceil(i!/2), i=0..n-k)))
end:
a:= n-> b(2*n, n):
seq(a(n), n=0..20);
MATHEMATICA
b[n_, k_] := b[n, k] = If[k<0 || k>n, 0, If[n==0, 1, Sum[Binomial[n-1, i]*b[n-1-i, k-1]*Ceiling[i!/2], {i, 0, n-k}]]]; a[n_] := b[2 n, n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 26 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 01 2015
STATUS
approved