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A055817 a(n) = T(2n+5,n), array T as in A055807.

%I A055817 #11 Feb 13 2021 21:30:13
%S A055817 1,63,448,2816,16896,99200,575872,3322112,19096064,109541824,
%T A055817 627653440,3594256896,20577979392,117814911744,674630384384,
%U A055817 3864033226240,22138650598400,126885674577728,727501822004416,4172725286118656
%N A055817 a(n) = T(2n+5,n), array T as in A055807.
%H A055817 G. C. Greubel, <a href="/A055817/b055817.txt">Table of n, a(n) for n = 0..250</a>
%F A055817 a(n) = (n+5)*hypergeom([-n-4, n], [2], -1) = Sum_{s=1..n+5} binomial(n+5,s) * binomial(s+n-2,n-1) for n >= 1. - _Petros Hadjicostas_, Feb 13 2021
%p A055817 T:= proc(i, j) option remember;
%p A055817       if j=0 then 1
%p A055817     elif i=0 then 0
%p A055817     else add(add(T(h,m), m=0..j), h=0..i-1)
%p A055817   fi; end:
%p A055817 seq(T(n+5, n), n=0..20); # _G. C. Greubel_, Jan 23 2020
%t A055817 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+5, n], {n,0,20}] (* _G. C. Greubel_, Jan 23 2020 *)
%o A055817 (Sage)
%o A055817 @CachedFunction
%o A055817 def T(i, j):
%o A055817     if (j==0): return 1
%o A055817     elif (i==0): return 0
%o A055817     else: return sum(sum(T(h,m) for m in (0..j)) for h in (0..i-1))
%o A055817 [T(n+5, n) for n in (0..20)] # _G. C. Greubel_, Jan 23 2020
%Y A055817 Cf. A055807, A055809, A055810, A055811, A055815, A055816.
%K A055817 nonn
%O A055817 0,2
%A A055817 _Clark Kimberling_, May 28 2000