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%I A370099 #7 Feb 10 2024 09:23:23
%S A370099 1,4,32,292,2816,28004,284000,2919620,30316544,317222212,3339504032,
%T A370099 35329425124,375282559232,4000059761572,42760427177696,
%U A370099 458259268924292,4921911787962368,52965710906750084,570951048018417440,6164049197776406180,66639047280436354816
%N A370099 a(n) = Sum_{k=0..n} binomial(2*n,k) * binomial(3*n-k-1,n-k).
%F A370099 a(n) = [x^n] ( (1+x)^2/(1-x)^2 )^n.
%F A370099 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x*(1-x)^2/(1+x)^2 ).
%o A370099 (PARI) a(n) = sum(k=0, n, binomial(2*n, k)*binomial(3*n-k-1, n-k));
%Y A370099 Cf. A370098, A370102.
%Y A370099 Cf. A032349.
%K A370099 nonn
%O A370099 0,2
%A A370099 _Seiichi Manyama_, Feb 10 2024

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