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%I #7 Jan 25 2024 07:49:40
%S 1,4,24,168,1284,10384,87360,756704,6703168,60444928,552990592,
%T 5120101760,47887472000,451759449600,4293634467840,41073654689280,
%U 395170166443008,3821262491103232,37118973530660864,362035991963869184,3544080121528001536
%N Expansion of (1/x) * Series_Reversion( x / ((1+x)^2+x^2)^2 ).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+2,k) * binomial(4*n-2*k+4,n-2*k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2+x^2)^2)/x)
%o (PARI) a(n) = sum(k=0, n\2, binomial(2*n+2, k)*binomial(4*n-2*k+4, n-2*k))/(n+1);
%Y Cf. A369502, A369504.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 25 2024
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