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Expansion of (1/x) * Series_Reversion( x * ((1-x)^3-x) ).
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%I #13 Dec 19 2024 07:23:11

%S 1,4,29,261,2627,28315,319648,3731037,44663058,545312504,6764556591,

%T 85015779095,1080185111768,13852183882612,179058158369828,

%U 2330621446075640,30519758687849439,401806204894374041,5315243189757111099,70613088335938995385,941714812929017751855

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

%H Seiichi Manyama, <a href="/A369215/b369215.txt">Table of n, a(n) for n = 0..868</a>

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

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

%Y Cf. A369114, A369161.

%Y Cf. A151374, A249924, A369216.

%Y Cf. A365764, A379171, A379172.

%Y Cf. A049140.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 16 2024