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A027048 a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A027023.

%I A027048 #13 Nov 05 2019 01:01:35
%S A027048 5,29,213,1633,12821,102369,826305,6724933,55108961,454279229,
%T A027048 3764205941,31334121045,261903891425,2197181330193,18494163039793,
%U A027048 156140262436597,1321876222268977,11219183496737037,95441562533950341,813656964557564557,6950294796825730249
%N A027048 a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A027023.
%H A027048 G. C. Greubel, <a href="/A027048/b027048.txt">Table of n, a(n) for n = 2..1000</a>
%p A027048 T:= proc(n, k) option remember;
%p A027048       if k<3 or k=2*n then 1
%p A027048     else add(T(n-1, k-j), j=1..3)
%p A027048       fi
%p A027048     end:
%p A027048 seq(add(T(n,k)*T(n,k+2), k=0..2*n-2), n=2..30); # _G. C. Greubel_, Nov 04 2019
%t A027048 T[n_, k_]:= T[n, k]= If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j,3}]]; Table[Sum[T[n,k]*T[n,k+2], {k,0,2*n-2}], {n,2,30}] (* _G. C. Greubel_, Nov 04 2019 *)
%o A027048 (Sage)
%o A027048 @CachedFunction
%o A027048 def T(n, k):
%o A027048     if (k<3 or k==2*n): return 1
%o A027048     else: return sum(T(n-1, k-j) for j in (1..3))
%o A027048 [sum(T(n,k)*T(n,k+2) for k in (0..2*n-2)) for n in (2..30)] # _G. C. Greubel_, Nov 04 2019
%K A027048 nonn
%O A027048 2,1
%A A027048 _Clark Kimberling_
%E A027048 More terms from _Sean A. Irvine_, Oct 22 2019