A371392 - OEIS

%I #12 Mar 21 2024 09:19:52

%S 1,7,68,769,9492,124014,1686120,23610565,338200148,4932348226,

%T 72993007672,1093371638954,16545598769416,252567107648604,

%U 3884497559034192,60136704175071789,936373570430169300,14654788984834217850,230405413840884827160,3637362857723455772670

%N Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+2*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} 2^k * binomial(3*(n+1),k) * binomial(2*n-k,n-k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+2*x)^3)/x)

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

%Y Cf. A047891, A371391.

%Y Cf. A113207.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 21 2024