cp's OEIS Frontend

A027272 Self-convolution of row n of array T given by A026552.

%I A027272 #14 Dec 19 2021 04:30:13
%S A027272 1,3,19,58,462,1608,13446,48924,417440,1553940,13409576,50618184,
%T A027272 440013462,1676640462,14649846820,56201554888,492944907180,
%U A027272 1900789437276,16721000706580,64734185205960,570792185166764,2216888144737508,19584623363041704,76265067399850848
%N A027272 Self-convolution of row n of array T given by A026552.
%H A027272 G. C. Greubel, <a href="/A027272/b027272.txt">Table of n, a(n) for n = 0..1000</a>
%F A027272 a(n) = Sum_{k=0..2*n} A026552(n, k)*A026552(n, 2*n-k).
%t A027272 T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+2)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k] + T[n-1, k-1], T[n-1, k-2] + T[n-1, k]]]]; (* T=A026552 *)
%t A027272 a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, Sum[T[n, k]*T[n, 2*n-k], {k, 0, 2*n}]];
%t A027272 Table[a[n], {n,0,40}] (* _G. C. Greubel_, Dec 18 2021 *)
%o A027272 (Sage)
%o A027272 @CachedFunction
%o A027272 def T(n,k): # T = A026552
%o A027272     if (k==0 or k==2*n): return 1
%o A027272     elif (k==1 or k==2*n-1): return (n+2)//2
%o A027272     elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o A027272     else: return T(n-1, k) + T(n-1, k-2)
%o A027272 @CachedFunction
%o A027272 def a(n): return sum( T(n,k)*T(n,2*n-k) for k in (0..2*n) )
%o A027272 [a(n) for n in (0..40)] # _G. C. Greubel_, Dec 18 2021
%Y A027272 Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026559, A026560, A026563, A026564, A026566, A026567, A027273, A027274, A027275, A027276.
%K A027272 nonn
%O A027272 0,2
%A A027272 _Clark Kimberling_
%E A027272 More terms from _Sean A. Irvine_, Oct 26 2019