OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..365
FORMULA
a(n) = A261780(n,n).
a(n) = [x^n] (1-x)^n/(2*(1-x)^n-1).
a(n) ~ n^n / (sqrt(2) * (log(2))^(n+1)). - Vaclav Kotesovec, Sep 21 2019
a(n) = Sum_{k>=1} (1/2)^k * binomial(k*n-1,n). - Seiichi Manyama, Aug 06 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-> A(n$2):
seq(a(n), n=0..20);
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_] := A[n, n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 24 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 31 2015
STATUS
approved