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%I #7 May 02 2024 09:46:17
%S 1,2,10,59,366,2332,15127,99388,659262,4405379,29611120,199986085,
%T 1356018339,9225340880,62941829996,430495159084,2950754125870,
%U 20263845589461,139393311839827,960318328961614,6624842357972916,45757925847607270,316401673996278705
%N Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^3) )^n.
%F a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(3*n-2*k-1,n-3*k).
%F The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x) * (1-x-x^3) ). See A368931.
%o (PARI) a(n, s=3, t=1, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t+u+1)*n-(s-1)*k-1, n-s*k));
%Y Cf. A368931, A372233.
%K nonn
%O 0,2
%A _Seiichi Manyama_, May 02 2024
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