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

0,2

Links

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

Formula

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

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 *)

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 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

Crossrefs

Cf. A026536.

Sequence in context: A150709 A130613 A143338 * A060414 A365806 A087241

Adjacent sequences: A027264 A027265 A027266 * A027268 A027269 A027270

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 26 2019

Status

approved