A369160 - OEIS

%I #10 Jan 15 2024 09:03:52

%S 1,2,7,30,144,742,4012,22458,129035,756602,4509141,27233726,166320987,

%T 1025356360,6372494608,39882831334,251146002084,1590079213920,

%U 10115878798130,64634124182670,414578955678690,2668578654593970,17232252926468640,111602332042716450

%N Expansion of (1/x) * Series_Reversion( x * ((1-x)^2-x^4) ).

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

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+k,k) * binomial(3*n-2*k+1,n-4*k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^2-x^4))/x)

%o (PARI) a(n) = sum(k=0, n\4, binomial(n+k, k)*binomial(3*n-2*k+1, n-4*k))/(n+1);

%Y Cf. A063021, A369102, A369161.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 15 2024