OFFSET
0,6
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..400
FORMULA
a(n) = Sum_{k=0..n-4} (n+k-1)!/(6*k!*(n-k-4)!*2^k).
a(n) = ( (n-3)*(4*n^2 - 24*n + 41)*a(n-1) + (n-2)*(2*n-5)*a(n-2) )/((n-4)*(2*n-7)), with a(0)=a(1)=a(2)=a(3)= 0, and a(4) = 1. - G. C. Greubel, Oct 10 2023
MAPLE
f3:=proc(n) local k; add((n+k-1)!/(6*(n-k-4)!*k!*2^k), k=0..n-4); end;
[seq(f3(n), n=0..60)];
MATHEMATICA
a[n_]:= a[n]= If[n<4, 0, If[n==4, 1, ((n-3)*(4*n^2-24*n+41)*a[n-1] + (n -2)*(2*n-5)*a[n-2])/((n-4)*(2*n-7))]]; (* a = A144506 *)
Table[a[n], {n, 0, 30}] (* G. C. Greubel, Oct 10 2023 *)
PROG
(Magma) I:=[0, 0, 0, 0, 1]; [n le 5 select I[n] else ((n-4)*(4*n^2-32*n+69)*Self(n-1) + (n-3)*(2*n-7)*Self(n-2))/((n-5)*(2*n-9)): n in [1..30]]; // A144506 // G. C. Greubel, Oct 10 2023
(SageMath)
@CachedFunction
def A144506(n): return sum(binomial(n-4, j)*rising_factorial(n-3, j+3)/(6*2^j) for j in range(n-3))
[A144506(n) for n in range(31)] # G. C. Greubel, Oct 10 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 14 2008
STATUS
approved