A369215
Expansion of (1/x) * Series_Reversion( x * ((1-x)^3-x) ).
Original entry on oeis.org
1, 4, 29, 261, 2627, 28315, 319648, 3731037, 44663058, 545312504, 6764556591, 85015779095, 1080185111768, 13852183882612, 179058158369828, 2330621446075640, 30519758687849439, 401806204894374041, 5315243189757111099, 70613088335938995385, 941714812929017751855
Offset: 0
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CoefficientList[InverseSeries[Series[x((1-x)^3-x),{x,0,21}],x]/x,x] (* Stefano Spezia, Mar 31 2025 *)
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3-x))/x)
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a(n) = sum(k=0, n, binomial(n+k, k)*binomial(4*n+2*k+2, n-k))/(n+1);
A369160
Expansion of (1/x) * Series_Reversion( x * ((1-x)^2-x^4) ).
Original entry on oeis.org
1, 2, 7, 30, 144, 742, 4012, 22458, 129035, 756602, 4509141, 27233726, 166320987, 1025356360, 6372494608, 39882831334, 251146002084, 1590079213920, 10115878798130, 64634124182670, 414578955678690, 2668578654593970, 17232252926468640, 111602332042716450
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^2-x^4))/x)
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a(n) = sum(k=0, n\4, binomial(n+k, k)*binomial(3*n-2*k+1, n-4*k))/(n+1);
A371435
Expansion of (1/x) * Series_Reversion( x * ((1-x)^3 + x^4) ).
Original entry on oeis.org
1, 3, 15, 91, 611, 4368, 32590, 250821, 1976441, 15865465, 129275835, 1066438399, 8888818659, 74743312480, 633272709348, 5400983817990, 46330852036920, 399479717666693, 3460229824525809, 30095179524446946, 262722158090170570, 2301201197665717770
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3+x^4))/x)
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a(n) = sum(k=0, n\4, (-1)^k*binomial(n+k, k)*binomial(4*n-k+2, n-4*k))/(n+1);
A369694
Expansion of (1/x) * Series_Reversion( x * ((1-x)^3-x^2) ).
Original entry on oeis.org
1, 3, 16, 106, 786, 6244, 51964, 447201, 3947306, 35538668, 325098696, 3013060258, 28232408848, 267003169668, 2545341982728, 24433290332007, 235967943943224, 2291147902820524, 22352525061549604, 219006814853751540, 2154083325737401740
Offset: 0
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CoefficientList[InverseSeries[Series[x*((1-x)^3 - x^2), {x, 0, 30}], x]/x, x](* Vaclav Kotesovec, Jan 29 2024 *)
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3-x^2))/x)
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a(n) = sum(k=0, n\2, binomial(n+k, k)*binomial(4*n+k+2, n-2*k))/(n+1);
Showing 1-4 of 4 results.