A370215 - OEIS

%I #9 Feb 12 2024 08:38:55

%S 1,2,6,26,134,702,3642,18916,99078,523448,2783406,14870418,79743002,

%T 428987236,2314194840,12514276476,67815709958,368183248722,

%U 2002240199040,10904629019548,59468066955534,324698112501166,1774806572174862,9710825272099992,53181284133726618

%N Coefficient of x^n in the expansion of ( (1+x)^2 / (1-x^3)^2 )^n.

%F a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(2*n,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^3)^2 ). See A369400.

%o (PARI) a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial(u*n, n-s*k));

%Y Cf. A369400.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 12 2024