OFFSET
5,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 5..800
FORMULA
a(n) ~ 16^n / (54*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015
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(n, 5):
seq(a(n), n=5..25);
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[n, 5];
a /@ Range[5, 25] (* Jean-François Alcover, Dec 28 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 31 2015
STATUS
approved