OFFSET
0,2
REFERENCES
V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..150
FORMULA
From Peter Bala, Feb 15 2022: (Start)
Conjectures:
a(2*n) = (-1)^(n+1)*(n + 1)*(2*n - 1)*(2*n)!.
a(2*n+1) = - 2*(2*n + 3)*(3*n - 2)*a(2*n-1) - 4*(n - 1)*(2*n + 3)*(4*n^2 - 1)*a(2*n-3) with a(1) = 3 and a(3) = -30. (End)
MAPLE
T:= proc(n, k) option remember;
if k=0 then 1
elif k=1 then n
else (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2)
fi; end:
seq(T(3, n), n=0..25); # G. C. Greubel, Jan 29 2020
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k==0, 1, If[k==1, n, (n-k+1)*T[n+1, k-1] - (k-1)*(n+1)* T[n+2, k-2]]]; Table[T[3, n], {n, 0, 25}] (* G. C. Greubel, Jan 29 2020 *)
PROG
(PARI) T(n, k) = if(k==0, 1, if(k==1, n, (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2) ));
vector(25, n, T(3, (n-1)) ) \\ G. C. Greubel, Jan 29 2020
(Magma)
function T(n, k)
if k eq 0 then return 1;
elif k eq 1 then return n;
else return (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2);
end if; return T; end function;
[T(3, n): n in [0..25]]; // G. C. Greubel, Jan 29 2020
(Sage)
@CachedFunction
def T(n, k):
if (k==0): return 1
elif (k==1): return n
else: return (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2)
[T(3, n) for n in (0..25)] # G. C. Greubel, Jan 29 2020
CROSSREFS
KEYWORD
sign
AUTHOR
Vincent v.d. Noort, Mar 21 2007
STATUS
approved