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%I #12 Jan 26 2024 11:10:33
%S 1,1,2,5,15,51,187,715,2800,11138,44846,182476,749566,3105575,
%T 12966165,54505650,230508612,980045835,4186600220,17960356014,
%U 77343359518,334217730014,1448771849516,6298222363395,27452466169243,119949953637406,525284132440963
%N Expansion of (1/x) * Series_Reversion( x * (1-x-x^4/(1-x)^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/4)} binomial(n+k,k) * binomial(2*n-k,n-4*k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^4/(1-x)^2))/x)
%o (PARI) a(n) = sum(k=0, n\4, binomial(n+k, k)*binomial(2*n-k, n-4*k))/(n+1);
%Y Cf. A063021, A367317, A367415.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jan 26 2024
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