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A027051 a(n) = T(n,2n-2), T given by A027023.

%I A027051 #15 Mar 08 2023 04:13:03
%S A027051 1,5,13,33,85,221,581,1545,4149,11237,30657,84169,232361,644573,
%T A027051 1795717,5021801,14091829,39665893,111965785,316857945,898797441,
%U A027051 2555025821,7277679961,20767821489,59365259065,169967668645,487356812589
%N A027051 a(n) = T(n,2n-2), T given by A027023.
%H A027051 G. C. Greubel, <a href="/A027051/b027051.txt">Table of n, a(n) for n = 2..750</a>
%F A027051 Conjecture: D-finite with recurrence n*a(n) +(-7*n+5)*a(n-1) +(13*n-18)*a(n-2) +(n-13)*a(n-3) +(-13*n+64)*a(n-4) +(3*n-25)*a(n-5) +(-n+2)*a(n-6) +3*(n-5)*a(n-7)=0. - _R. J. Mathar_, Jun 24 2020
%F A027051 a(n) ~ 3^(n + 5/2) / (2 * sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Mar 08 2023
%p A027051 T:= proc(n, k) option remember;
%p A027051       if k<3 or k=2*n then 1
%p A027051     else add(T(n-1, k-j), j=1..3)
%p A027051       fi
%p A027051     end:
%p A027051 seq(T(n,2*n-2), n=2..30); # _G. C. Greubel_, Nov 05 2019
%t A027051 T[n_, k_]:= T[n, k]= If[n<0, 0, If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j, 3}]]]; Table[T[n, 2*n-2], {n,2,30}] (* _G. C. Greubel_, Nov 05 2019 *)
%o A027051 (Sage)
%o A027051 @CachedFunction
%o A027051 def T(n, k):
%o A027051     if (k<3 or k==2*n): return 1
%o A027051     else: return sum(T(n-1, k-j) for j in (1..3))
%o A027051 [T(n, 2*n-2) for n in (2..30)] # _G. C. Greubel_, Nov 05 2019
%Y A027051 Cf. A027023.
%K A027051 nonn
%O A027051 2,2
%A A027051 _Clark Kimberling_