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A026962 a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026626.

%I A026962 #12 Jun 23 2024 22:01:18
%S A026962 1,6,24,108,406,1572,5961,22788,87209,335010,1290376,4983162,19286891,
%T A026962 74797176,290586771,1130716508,4406049037,17191077082,67152699384,
%U A026962 262594530318,1027851765350,4026831276662,15788979175102,61954847930374,243278117470476,955907159445522
%N A026962 a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026626.
%H A026962 G. C. Greubel, <a href="/A026962/b026962.txt">Table of n, a(n) for n = 1..1000</a>
%t A026962 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 A026962 A262962[n_]:=Sum[T[n,k]*T[n,k+1], {k,0,n-1}];
%t A026962 Table[A262962[n], {n,40}] (* _G. C. Greubel_, Jun 23 2024 *)
%o A026962 (SageMath)
%o A026962 @CachedFunction
%o A026962 def T(n, k): # T = A026626
%o A026962     if (k==0 or k==n): return 1
%o A026962     elif (k==1 or k==n-1): return int(3*n//2)
%o A026962     else: return T(n-1, k-1) + T(n-1, k)
%o A026962 def A262962(n): return sum( T(n,k)*T(n,k+1) for k in range(n))
%o A026962 [A262962(n) for n in range(1,41)] # _G. C. Greubel_, Jun 23 2024
%Y A026962 Cf. A026626, A026627, A026628, A026629, A026630, A026631, A026632.
%Y A026962 Cf. A026633, A026634, A026635, A026636, A026961, A026963, A026964.
%Y A026962 Cf. A026965.
%K A026962 nonn
%O A026962 1,2
%A A026962 _Clark Kimberling_
%E A026962 More terms from _Sean A. Irvine_, Oct 20 2019