OFFSET
0,4
COMMENTS
See A129462 for the M. Bruschi et al. reference.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..250
FORMULA
a(n) = Sum_{k=0..n} A129462(n,k), n >= 0.
From Vaclav Kotesovec, Aug 24 2016: (Start)
a(n) = 2*(n-2)*(n-1)*a(n-1) - (n-3)^2*(n-1)^2*a(n-2).
a(n) ~ c * n^(2*n+(sqrt(5)-3)/2) / exp(2*n), where c = -2.3203776630375605070105975273368548459...
(End)
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k<0 || k>n, 0, If[n==0, 1, (2*(n-1)*(n-2) - 1)*T[n-1, k] -((n-1)*(n-3))^2*T[n-2, k] +T[n-1, k-1] ]]; (* T=A129462 *)
Table[A129463[n], {n, 0, 40}] (* G. C. Greubel, Feb 08 2024 *)
PROG
(SageMath)
@CachedFunction
def T(n, k): # T = A129462
if (k<0 or k>n): return 0
elif (n==0): return 1
else: return (2*(n-1)*(n-2)-1)*T(n-1, k) - ((n-1)*(n-3))^2*T(n-2, k) + T(n-1, k-1)
def A129463(n): return sum(T(n, k) for k in range(n+1))
[A129463(n) for n in range(41)] # G. C. Greubel, Feb 08 2024
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, May 04 2007
STATUS
approved