OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
a(n) = A261781(2n,n).
a(n) ~ c * d^n * n!^2 / n, where d = -4 / (log(2)^2 * LambertW(-2*exp(-2)) * (2 + LambertW(-2*exp(-2)))) = 12.85568917366612131932660300054233483234... and c = 0.25886492311146555025177523170232718427705044811049100445591... . - Vaclav Kotesovec, Feb 18 2017, updated Apr 20 2024
MAPLE
A:= proc(n, k) option remember; `if`(n=0, 1,
add(A(n-j, k)*binomial(j+k-1, k-1), j=1..n))
end:
a:= n-> add(A(2*n, n-i)*(-1)^i*binomial(n, i), i=0..n):
seq(a(n), n=0..15);
MATHEMATICA
A[n_, k_] := A[n, k] = If[n == 0, 1, Sum[A[n - j, k]*Binomial[j + k - 1, k - 1], {j, 1, n}]]; a[n_] := Sum[A[2*n, n - i]*(-1)^i*Binomial[n, i], {i, 0, n}]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Feb 25 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 31 2015
STATUS
approved