cp's OEIS Frontend

A027073 a(n) = Sum_{k=0..n} T(n,k) * T(n,2n-k), with T given by A027052.

%I A027073 #13 Nov 07 2019 08:28:48
%S A027073 1,1,2,8,31,129,510,1970,7513,28253,105176,388330,1423691,5188577,
%T A027073 18812848,67907520,244160177,874821817,3124747792,11130097846,
%U A027073 39544807851,140180597013,495886522916,1750852227736,6171019594129
%N A027073 a(n) = Sum_{k=0..n} T(n,k) * T(n,2n-k), with T given by A027052.
%H A027073 G. C. Greubel, <a href="/A027073/b027073.txt">Table of n, a(n) for n = 0..1000</a>
%p A027073 T:= proc(n, k) option remember;
%p A027073       if k<0 or k>2*n then 0
%p A027073     elif k=0 or k=2 or k=2*n then 1
%p A027073     elif k=1 then 0
%p A027073     else add(T(n-1, k-j), j=1..3)
%p A027073       fi
%p A027073     end:
%p A027073 seq( add(T(n,k)*T(n,2*n-k), k=0..n), n=0..30); # _G. C. Greubel_, Nov 06 2019
%t A027073 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, n}], {n,0,30}] (* _G. C. Greubel_, Nov 06 2019 *)
%o A027073 (Sage)
%o A027073 @CachedFunction
%o A027073 def T(n, k):
%o A027073     if (k<0 or k>2*n): return 0
%o A027073     elif (k==0 or k==2 or k==2*n): return 1
%o A027073     elif (k==1): return 0
%o A027073     else: return sum(T(n-1, k-j) for j in (1..3))
%o A027073 [sum(T(n,k)*T(n,2*n-k) for k in (0..n)) for n in (0..30)] # _G. C. Greubel_, Nov 06 2019
%K A027073 nonn
%O A027073 0,3
%A A027073 _Clark Kimberling_