A369215 Expansion of (1/x) * Series_Reversion( x * ((1-x)^3-x) ).
1, 4, 29, 261, 2627, 28315, 319648, 3731037, 44663058, 545312504, 6764556591, 85015779095, 1080185111768, 13852183882612, 179058158369828, 2330621446075640, 30519758687849439, 401806204894374041, 5315243189757111099, 70613088335938995385, 941714812929017751855
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..868
- Index entries for reversions of series
Crossrefs
Programs
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Mathematica
CoefficientList[InverseSeries[Series[x((1-x)^3-x),{x,0,21}],x]/x,x] (* Stefano Spezia, Mar 31 2025 *) -
PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3-x))/x) -
PARI
a(n) = sum(k=0, n, binomial(n+k, k)*binomial(4*n+2*k+2, n-k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+k,k) * binomial(4*n+2*k+2,n-k).