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%I #11 Apr 30 2024 06:08:36
%S 1,1,3,13,55,231,981,4215,18271,79735,349843,1541783,6820045,30263689,
%T 134658681,600578373,2684116863,12017803439,53895617379,242054324055,
%U 1088530440315,4900978877115,22089865194543,99662269990363,450049706481181,2033999993960581
%N Coefficient of x^n in the expansion of ( (1-x+x^3) / (1-x)^2 )^n.
%F a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(2*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)^2 / (1-x+x^3) ).
%o (PARI) a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((u-t+1)*n-(s-1)*k-1, n-s*k));
%Y Cf. A372413, A372415.
%Y Cf. A049128.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Apr 29 2024
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