OFFSET
0,2
FORMULA
From Vaclav Kotesovec, Feb 17 2024: (Start)
Recurrence: n^3*a(n) = 8*(24*n^3 - 12*n^2 - 22*n + 19)*a(n-1) - 3072*(n-1)*(4*n^2 - 7)*a(n-2) + 131072*(n-2)*(n-1)*(2*n + 3)*a(n-3).
a(n) ~ 64^n * log(n)^2 * sqrt(n) / Pi^(5/2) * (1 + c1/log(n) + c2/log(n)^2), where c1 = -3.755213781237809328111261876504370048707679178356... and c2 = 14.59060543515491211393377346917067214120336575838... (End)
MAPLE
a := n -> 64^n*hypergeom([-1/2, -1/2, -1/2, -n], [1, 1, 1], 1):
seq(simplify(a(n)), n = 0..15);
MATHEMATICA
a[n_] := 64^n * HypergeometricPFQ[{-1/2, -1/2, -1/2, -n}, {1, 1, 1}, 1]; Array[a, 16, 0] (* Amiram Eldar, Nov 12 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Nov 12 2022
STATUS
approved