A026529 a(n) = T(2*n-1, n-2), where T is given by A026519.

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

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

Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026526, A026527, A026528, A026530, A026531, A026533, A026534, A027262, A027263, A027264, A027265, A027266.

Cf. A026552.

Sequence in context: A196907 A116427 A008827 * A363881 A357870 A286182

Adjacent sequences: A026526 A026527 A026528 * A026530 A026531 A026532

Keyword

nonn

Author

Clark Kimberling

Extensions

Terms a(20) onward added by G. C. Greubel, Dec 20 2021

Status

approved