A371394 - OEIS

%I #11 Mar 21 2024 09:20:11

%S 1,10,137,2174,37562,686004,13027065,254641398,5089756958,

%T 103552330700,2137385941418,44647634773420,942085264713556,

%U 20050276273007080,429913404536172633,9278142975370425510,201383222768034837750,4393265621094818733660

%N Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+3*x)^3 ).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

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

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+3*x)^3)/x)

%o (PARI) a(n) = sum(k=0, n, 3^k*binomial(3*(n+1), k)*binomial(2*n-k, n-k))/(n+1);

%Y Cf. A082298, A371393.

%Y Cf. A365816.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 21 2024