OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..250
FORMULA
a(n) = A256117(2n,n).
a(n) ~ c * d^n * n! / n^(5/2), where d = A256254 = 98.82487375173568573170688..., c = -sqrt(2) * LambertW(-2*exp(-2)) / (16 * Pi^(3/2) * sqrt(1 + LambertW(-2*exp(-2)))) = 0.008372249434869139279228556376854454452398... . - Vaclav Kotesovec, Jun 01 2015, updated Sep 27 2023
MAPLE
A:= proc(n, k) option remember; `if`(n=0, 1, k/n*
add(binomial(2*n, j)*(n-j)*(k-1)^j, j=0..n-1))
end:
T:= (n, k)-> add((-1)^i*A(n, k-i)/(i!*(k-i)!), i=0..k):
a:= n-> T(2*n, n):
seq(a(n), n=0..20);
MATHEMATICA
A[n_, k_] := A[n, k] = If[n==0, 1, (k/n) Sum[Binomial[2n, j] (n-j) If[j==0, 1, (k-1)^j], {j, 0, n-1}]];
T[n_, k_] := Sum[(-1)^i A[n, k-i]/(i! (k-i)!), {i, 0, k}];
a[n_] := T[2n, n];
a /@ Range[0, 20] (* Jean-François Alcover, Dec 21 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 31 2015
STATUS
approved