OFFSET
2,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 2..1000
FORMULA
a(n) = A026519(2*n-1, n-2).
a(n) = A026552(2*n-1, n-2).
a(n) = Sum_{i=0..floor(n/2)} C(n-1, i-1)*Sum_{j=0..n} C(j, n-j+2*i)*C(n, j). - Vladimir Kruchinin, Jan 16 2015
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k], T[n-1, k-1] + T[n-1, k-2] + T[n-1, k] ]]]]; (* T = A026519 *)
a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, T[2*n-1, n-2] ];
Table[a[n], {n, 2, 40}] (* G. C. Greubel, Dec 20 2021 *)
PROG
(Maxima)
a(n):=sum(binomial(n-1, i-1)*sum(binomial(j, n-j+2*i)*binomial(n, j), j, 0, n), i, 1, n/2); /* Vladimir Kruchinin, Jan 16 2015 */
(Sage)
@CachedFunction
def T(n, k): # T = A026519
if (k<0 or k>2*n): return 0
elif (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n+1)//2
elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
[T(2*n-1, n-2) for n in (2..40)] # G. C. Greubel, Dec 20 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(20) onward added by G. C. Greubel, Dec 20 2021
STATUS
approved