%I #10 Nov 07 2019 08:28:53

%S 1,2,3,12,53,222,899,3540,13657,51882,194727,723760,2668453,9771870,

%T 35577935,128887616,464885073,1670362418,5981289455,21352860808,

%U 76020123293,269977176422,956644165503,3382864303648,11940005836537

%N a(n) = self-convolution of row n of array T given by A027052.

%H G. C. Greubel, <a href="/A027072/b027072.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = Sum_{k=0..2*n} T(n,k)*T(n,2*n-k), where T = A027052. - _G. C. Greubel_, Nov 06 2019

%p T:= proc(n, k) option remember;

%p if k<0 or k>2*n then 0

%p elif k=0 or k=2 or k=2*n then 1

%p elif k=1 then 0

%p else add(T(n-1, k-j), j=1..3)

%p fi

%p end:

%p seq( add(T(n,k)*T(n,2*n-k), k=0..2*n), n=0..30); # _G. C. Greubel_, Nov 06 2019

%t T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]]; Table[Sum[T[n,k]*T[n,2*n-k], {k,0,2*n}], {n,0,30}] (* _G. C. Greubel_, Nov 06 2019 *)

%o (Sage)

%o @CachedFunction

%o def T(n, k):

%o if (k<0 or k>2*n): return 0

%o elif (k==0 or k==2 or k==2*n): return 1

%o elif (k==1): return 0

%o else: return sum(T(n-1, k-j) for j in (1..3))

%o [sum(T(n,k)*T(n,2*n-k) for k in (0..2*n)) for n in (0..30)] # _G. C. Greubel_, Nov 06 2019

%K nonn

%O 0,2

%A _Clark Kimberling_