A027267 a(n) = self-convolution of row n of array T given by A026536.

1, 2, 8, 26, 196, 692, 5774, 21142, 180772, 675344, 5837908, 22087716, 192239854, 733698032, 6416509142, 24645099530, 216309089956, 834847581048, 7347943049432, 28467646552432, 251119894730596, 975892708569952, 8624336421678788, 33600628889991916, 297394187356638766

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A026536.

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,2*n-k], {k,0,2*n}], {n,0,40}] (* 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 A027267(n): return sum(T(n,k)*T(n,2*n-k) for k in (0..2*n))
[A027267(n) for n in (0..40)] # G. C. Greubel, Apr 12 2022

Formula

a(n) = Sum_{k=0..2*n} A026536(n, k)*A026536(n, 2*n-k). - G. C. Greubel, Apr 12 2022

Extensions

More terms from Sean A. Irvine, Oct 26 2019