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

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026536, A027267, A027268, A027270.

Programs

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 *)

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

Formula

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

Extensions

More terms from Sean A. Irvine, Oct 26 2019

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