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A104979 Semidiagonal sums of triangle A104978: a(n) = Sum_{k=0..[n/2]} A104978(n-k,n-2*k).

%I A104979 #10 Sep 08 2022 08:45:17
%S A104979 1,1,4,17,85,459,2614,15454,93947,583568,3687761,23633072,153227250,
%T A104979 1003281314,6624658716,44062205158,294938814921,1985330061570,
%U A104979 13430612284606,91262392343333,622624395706714,4263163419492661
%N A104979 Semidiagonal sums of triangle A104978: a(n) = Sum_{k=0..[n/2]} A104978(n-k,n-2*k).
%H A104979 G. C. Greubel, <a href="/A104979/b104979.txt">Table of n, a(n) for n = 0..1000</a>
%F A104979 a(n) = Sum_{k=0..floor(n/2)} A104978(n-k, n-2*k).
%F A104979 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-4*k, 3*n-5*k)*binomial(3*n-5*k, n-2*k)/(2*n-3*k+1).
%F A104979 G.f. satisfies: A(x) = 1 + x*A(x)^3 + x^2*A(x)^2. - _Paul D. Hanna_, May 27 2010
%t A104979 Table[Sum[Binomial[3*n-4*k, 3*n-5*k]*Binomial[3*n-5*k, n-2*k]/(2*n-3*k+1), {k,0,n/2}], {n,0,30}] (* _G. C. Greubel_, Jun 08 2021 *)
%o A104979 (PARI) {a(n)=sum(k=0,n\2, binomial(3*n-4*k,3*n-5*k)*binomial(3*n-5*k,n-2*k)/(2*n-3*k+1))}
%o A104979 (Magma)
%o A104979 A104979:= func< n | (&+[Binomial(3*n-4*k, 3*n-5*k)*Binomial(3*n-5*k, n-2*k)/(2*n-3*k+1): k in [0..Floor(n/2)]]) >;
%o A104979 [A104979(n): n in [0..30]]; // _G. C. Greubel_, Jun 08 2021
%o A104979 (Sage)
%o A104979 def A104979(n): return sum( binomial(3*n-4*k, 3*n-5*k)*binomial(3*n-5*k, n-2*k)/(2*n-3*k+1) for k in (0..n//2) )
%o A104979 [A104979(n) for n in (0..30)] # _G. C. Greubel_, Jun 08 2021
%Y A104979 Cf. A104978.
%K A104979 nonn
%O A104979 0,3
%A A104979 _Paul D. Hanna_, Mar 30 2005