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%I #13 Feb 13 2024 10:56:20
%S 1,3,23,192,1687,15253,140504,1311292,12357015,117318162,1120436273,
%T 10752242592,103596191608,1001494496863,9709576926716,94369011385192,
%U 919175964169623,8970063281146830,87685232945278010,858446087522807784,8415669293820893937
%N a(n) = Sum_{k=0..n} (-1)^k * binomial(n+k-1,k) * binomial(5*n-k-1,n-k).
%F a(n) = [x^n] 1/( (1+x) * (1-x)^4 )^n.
%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)^4 ). See A365752.
%F a(n) = Sum_{k=0..floor(n/2)} binomial(n+k-1,k) * binomial(4*n-2*k-1,n-2*k).
%o (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n+k-1, k)*binomial(5*n-k-1, n-k));
%o (PARI) a(n, s=2, t=1, u=3) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((u+1)*n-s*k-1, n-s*k));
%Y Cf. A348410, A352373.
%Y Cf. A365752.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Feb 10 2024
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