cp's OEIS Frontend

A027215 Self-convolution of row n of array T given by A026736.

%I A027215 #9 Jul 20 2019 08:09:51
%S A027215 1,2,6,20,78,282,1187,4428,19175,72820,319493,1227712,5424359,
%T A027215 21018514,93252862,363563668,1617342486,6334904252,28232695584,
%U A027215 110982722888,495257577162
%N A027215 Self-convolution of row n of array T given by A026736.
%H A027215 G. C. Greubel, <a href="/A027215/b027215.txt">Table of n, a(n) for n = 0..1000</a>
%t A027215 T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[EvenQ[n] && k==(n-2)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k]]];
%t A027215 Table[Sum[T[n, k]*T[n, n-k], {k,0,n}], {n,0,40}] (* _G. C. Greubel_, Jul 19 2019 *)
%o A027215 (PARI) T(n, k) = if(k==n || k==0, 1, k==n-1, n, if((n%2)==0 && k==(n-2)/2, T(n-1, k-1) + T(n-2, k-1) + T(n-1, k), T(n-1, k-1) + T(n-1, k) ));
%o A027215 vector(21, n, n--; sum(k=0, n, T(n, k)*T(n,n-k)) ) \\ _G. C. Greubel_, Jul 19 2019
%o A027215 (Sage)
%o A027215 @CachedFunction
%o A027215 def T(n, k):
%o A027215     if (k==0 or k==n): return 1
%o A027215     if (k==n-1): return n
%o A027215     elif (mod(n, 2)==0 and k==(n-2)/2): return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k)
%o A027215     else: return T(n-1, k-1) + T(n-1, k)
%o A027215 [sum(T(n,k)*T(n,n-k) for k in (0..n)) for n in (0..40)] # _G. C. Greubel_, Jul 19 2019
%o A027215 (GAP)
%o A027215 T:= function(n, k)
%o A027215     if k=0 or k=n then return 1;
%o A027215     elif k=n-1 then return n;
%o A027215     elif (n mod 2)=0 and k=Int((n-2)/2) then return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k);
%o A027215     else return T(n-1, k-1) + T(n-1, k);
%o A027215     fi;
%o A027215   end;
%o A027215 List([0..20], n-> Sum([0..n], k-> T(n, k)*T(n,n-k) )); # _G. C. Greubel_, Jul 19 2019
%Y A027215 Cf. A026736.
%K A027215 nonn
%O A027215 0,2
%A A027215 _Clark Kimberling_