A371435 - OEIS

%I #10 Mar 23 2024 11:07:11

%S 1,3,15,91,611,4368,32590,250821,1976441,15865465,129275835,

%T 1066438399,8888818659,74743312480,633272709348,5400983817990,

%U 46330852036920,399479717666693,3460229824525809,30095179524446946,262722158090170570,2301201197665717770

%N Expansion of (1/x) * Series_Reversion( x * ((1-x)^3 + 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)} (-1)^k * binomial(n+k,k) * binomial(4*n-k+2,n-4*k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3+x^4))/x)

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

%Y Cf. A369124, A371432.

%Y Cf. A369161.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 23 2024