%I #12 Jun 23 2024 22:01:37

%S 1,8,52,224,987,3980,16057,63732,252424,996332,3927977,15471622,

%T 60915547,239794516,943946193,3716205884,14632901696,57631689776,

%U 227042423404,894698122022,3526753844436,13906101471344,54848887043366,216402159510134,854053133294062,3371593602442500

%N a(n) = Sum_{k=0..n-2} T(n,k) * T(n,k+2), with T given by A026626.

%H G. C. Greubel, <a href="/A026963/b026963.txt">Table of n, a(n) for n = 2..1000</a>

%t T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[k==1 || k==n-1, Floor[3*n/2], T[n-1,k-1] +T[n-1,k]]]; (* T = A026626 *)

%t A262963[n_]:= Sum[T[n,k]*T[n,k+2], {k,0,n-2}];

%t Table[A262963[n], {n,2,40}] (* _G. C. Greubel_, Jun 23 2024 *)

%o (SageMath)

%o @CachedFunction

%o def T(n, k): # T = A026626

%o if (k==0 or k==n): return 1

%o elif (k==1 or k==n-1): return int(3*n//2)

%o else: return T(n-1, k-1) + T(n-1, k)

%o def A262963(n): return sum( T(n,k)*T(n,k+2) for k in range(n-1))

%o [A262963(n) for n in range(2,41)] # _G. C. Greubel_, Jun 23 2024

%Y Cf. A026626, A026627, A026628, A026629, A026630, A026631, A026632.

%Y Cf. A026633, A026634, A026635, A026636, A026961, A026962, A026964.

%Y Cf. A026965.

%K nonn

%O 2,2

%A _Clark Kimberling_

%E More terms from _Sean A. Irvine_, Oct 20 2019