A368938 - OEIS

%I #10 Jan 10 2024 08:00:49

%S 1,3,14,78,479,3129,21332,150057,1081118,7937589,59174752,446744610,

%T 3408616155,26242751046,203615759472,1590550846398,12498584431503,

%U 98731454253945,783581338236326,6245066800130298,49961547869830135,401076129627216180,3229808459696023980

%N Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x+x^2) ).

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(n+k,k) * binomial(4*n-k+2,n-2*k).

%o (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n+k, k)*binomial(4*n-k+2, n-2*k))/(n+1);

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

%Y Cf. A129442, A368934.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 10 2024