Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #12 Jun 23 2024 22:01:18
%S 1,6,24,108,406,1572,5961,22788,87209,335010,1290376,4983162,19286891,
%T 74797176,290586771,1130716508,4406049037,17191077082,67152699384,
%U 262594530318,1027851765350,4026831276662,15788979175102,61954847930374,243278117470476,955907159445522
%N a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026626.
%H G. C. Greubel, <a href="/A026962/b026962.txt">Table of n, a(n) for n = 1..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 A262962[n_]:=Sum[T[n,k]*T[n,k+1], {k,0,n-1}];
%t Table[A262962[n], {n,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 A262962(n): return sum( T(n,k)*T(n,k+1) for k in range(n))
%o [A262962(n) for n in range(1,41)] # _G. C. Greubel_, Jun 23 2024
%Y Cf. A026626, A026627, A026628, A026629, A026630, A026631, A026632.
%Y Cf. A026633, A026634, A026635, A026636, A026961, A026963, A026964.
%Y Cf. A026965.
%K nonn
%O 1,2
%A _Clark Kimberling_
%E More terms from _Sean A. Irvine_, Oct 20 2019