A027269 a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A026536.

1, 5, 19, 150, 561, 4797, 18089, 156900, 596674, 5205950, 19932353, 174609162, 672106267, 5906040623, 22829936683, 201114700568, 780077588440, 6885880226784, 26784015828458, 236826459554380, 923352937530146, 8175978023317170, 31940549289135429, 283166067626865540

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..500

Formula

a(n) = Sum_{k=0..2n-2} A026536(n,k) * A026536(n,k+2).

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n], T[n-1, k-2] +T[n-1, k-1] +T[n-1, k], T[n-1, k-2] +T[n-1, k]] ]];
Table[Sum[T[n, k]*T[n, k+2], {k, 0, 2*n-2}], {n, 40}] (* G. C. Greubel, Apr 12 2022 *)

Prog

(SageMath)
@CachedFunction
def T(n, k): # A026536
    if k < 0 or n < 0: return 0
    elif k == 0 or k == 2*n: return 1
    elif k == 1 or k == 2*n-1: return n//2
    elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
    return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
def A027269(n): return sum(T(n, k)*T(n, k+2) for k in (0..2*n-2))
[A027269(n) for n in (1..40)] # G. C. Greubel, Apr 12 2022

Crossrefs

Cf. A026536, A027267, A027268, A027270.

Sequence in context: A354843 A187018 A193287 * A082790 A145935 A024529

Adjacent sequences: A027266 A027267 A027268 * A027270 A027271 A027272

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 26 2019

a(1) = 1 prepended by G. C. Greubel, Apr 12 2022

Status

approved