OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
MATHEMATICA
T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[EvenQ[n] && k==(n-2)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k]]];
Table[Sum[T[n, k]*T[n, n-k], {k, 0, n}], {n, 0, 40}] (* G. C. Greubel, Jul 19 2019 *)
PROG
(PARI) T(n, k) = if(k==n || k==0, 1, k==n-1, n, if((n%2)==0 && k==(n-2)/2, T(n-1, k-1) + T(n-2, k-1) + T(n-1, k), T(n-1, k-1) + T(n-1, k) ));
vector(21, n, n--; sum(k=0, n, T(n, k)*T(n, n-k)) ) \\ G. C. Greubel, Jul 19 2019
(Sage)
@CachedFunction
def T(n, k):
if (k==0 or k==n): return 1
if (k==n-1): return n
elif (mod(n, 2)==0 and k==(n-2)/2): return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k)
else: return T(n-1, k-1) + T(n-1, k)
[sum(T(n, k)*T(n, n-k) for k in (0..n)) for n in (0..40)] # G. C. Greubel, Jul 19 2019
(GAP)
T:= function(n, k)
if k=0 or k=n then return 1;
elif k=n-1 then return n;
elif (n mod 2)=0 and k=Int((n-2)/2) then return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k);
else return T(n-1, k-1) + T(n-1, k);
fi;
end;
List([0..20], n-> Sum([0..n], k-> T(n, k)*T(n, n-k) )); # G. C. Greubel, Jul 19 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved