A026962 - OEIS

%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