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A055816 a(n) = T(2*n+4,n), array T as in A055807.

%I A055816 #11 Feb 13 2021 21:27:34
%S A055816 1,31,192,1120,6400,36288,205184,1159488,6554880,37088480,210075712,
%T A055816 1191254688,6762782208,38434677120,218663320320,1245254943872,
%U A055816 7098135387648,40495661150112,231220652273600,1321222104326880
%N A055816 a(n) = T(2*n+4,n), array T as in A055807.
%H A055816 G. C. Greubel, <a href="/A055816/b055816.txt">Table of n, a(n) for n = 0..250</a>
%F A055816 a(n) = (n+4)*hypergeom([-n -3, n], [2], -1) = Sum_{s=1..n+4} binomial(n+4,s)*binomial(s+n-2,n-1) for n >= 1. - _Petros Hadjicostas_, Feb 13 2021
%p A055816 T:= proc(i, j) option remember;
%p A055816       if j=0 then 1
%p A055816     elif i=0 then 0
%p A055816     else add(add(T(h,m), m=0..j), h=0..i-1)
%p A055816   fi; end:
%p A055816 seq(T(n+4, n), n=0..20); # _G. C. Greubel_, Jan 23 2020
%t A055816 T[i_, j_]:= T[i, j]= If[j==0, 1, If[i==0, 0, Sum[T[h, m], {h,0,i-1}, {m,0,j}]]]; Table[T[n+4, n], {n,0,20}] (* _G. C. Greubel_, Jan 23 2020 *)
%o A055816 (Sage)
%o A055816 @CachedFunction
%o A055816 def T(i, j):
%o A055816     if (j==0): return 1
%o A055816     elif (i==0): return 0
%o A055816     else: return sum(sum(T(h,m) for m in (0..j)) for h in (0..i-1))
%o A055816 [T(n+4, n) for n in (0..20)] # _G. C. Greubel_, Jan 23 2020
%Y A055816 Cf. A055807, A055809, A055810, A055811, A055815, A055817.
%K A055816 nonn
%O A055816 0,2
%A A055816 _Clark Kimberling_, May 28 2000