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A026529
a(n) = T(2*n-1, n-2), where T is given by A026519.
20
1, 3, 13, 50, 205, 833, 3437, 14232, 59301, 248050, 1041469, 4385888, 18519306, 78376403, 332370925, 1412000824, 6008104249, 25601113893, 109229104313, 466577280830, 1995120743749, 8539562784258, 36583756253885, 156854365793800, 673028595199000, 2889847430222961, 12416501973954798, 53381063233213198
OFFSET
2,2
LINKS
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
KEYWORD
nonn
EXTENSIONS
Terms a(20) onward added by G. C. Greubel, Dec 20 2021
STATUS
approved