OFFSET
0,6
REFERENCES
V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.
LINKS
G. C. Greubel, Antidiagonals n = 0..100, flattened
FORMULA
See A127080 for e.g.f.
EXAMPLE
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(seq(T(n-k, k), k=0..n), n=0..12); # G. C. Greubel, Jan 28 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[n-k, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jan 28 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) )); \\ G. C. Greubel, Jan 28 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(n-k, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jan 28 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(n-k, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jan 28 2020
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Vincent v.d. Noort, Mar 24 2007
EXTENSIONS
More terms added by G. C. Greubel, Jan 28 2020
STATUS
approved