A371433 - OEIS

%I #11 Mar 23 2024 11:04:19

%S 1,2,5,11,11,-77,-704,-3795,-15686,-48598,-74009,376623,4438840,

%T 27458060,126898948,440550682,849522927,-2621906045,-39993434701,

%U -270428078305,-1339005344985,-5014789377825,-11407684195950,18849058485855,417417757017612,3058172078113944

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

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

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

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

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

%Y Cf. A371434, A371435.

%Y Cf. A369215.

%K sign

%O 0,2

%A _Seiichi Manyama_, Mar 23 2024