|
%I #8 Mar 03 2024 09:53:09
%S 1,1,0,-2,-2,6,19,1,-98,-170,268,1464,967,-7253,-19035,11497,142894,
%T 186814,-592148,-2327480,-371472,14922592,30367918,-44517534,
%U -291059645,-242260229,1550840094,4611423196,-2050694753,-36095033685,-54276040088,150373292998
%N Expansion of (1/x) * Series_Reversion( x/(x+1/(1+x^2)) ).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n,2*k) * binomial(3*k,k)/(2*k+1).
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x/(x+1/(1+x^2)))/x)
%o (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n, 2*k)*binomial(3*k, k)/(2*k+1));
%Y Cf. A370837, A370838.
%Y Cf. A049130, A370799.
%K sign
%O 0,4
%A _Seiichi Manyama_, Mar 03 2024
|
