A369114
Expansion of (1/x) * Series_Reversion( x * ((1-x)^3-x^3) ).
Original entry on oeis.org
1, 3, 15, 92, 630, 4620, 35494, 282015, 2298417, 19108265, 161418543, 1381606044, 11955789440, 104427062460, 919430773992, 8151530382264, 72711166411422, 652075100808960, 5875868463764446, 53175058170610530, 483082193418731280, 4404057834071995110
Offset: 0
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A369114 := proc(n)
add(binomial(n+k,k) * binomial(4*n+2,n-3*k),k=0..floor(n/3)) ;
%/(n+1) ;
end proc;
seq(A369114(n),n=0..70) ; # R. J. Mathar, Jan 25 2024
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3-x^3))/x)
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a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(4*n+2, n-3*k))/(n+1);
A369124
Expansion of (1/x) * Series_Reversion( x * ((1-x)^4+x^4) ).
Original entry on oeis.org
1, 4, 26, 204, 1770, 16352, 157696, 1569096, 15988652, 165998624, 1749696208, 18673883696, 201394693864, 2191421381632, 24028822589440, 265238416143584, 2944999336948944, 32869042668479424, 368551132961138784, 4149643380825661824, 46897527236429235520
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^4+x^4))/x)
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a(n) = sum(k=0, n\4, (-1)^k*binomial(n+k, k)*binomial(5*n+3, n-4*k))/(n+1);
A369161
Expansion of (1/x) * Series_Reversion( x * ((1-x)^3-x^4) ).
Original entry on oeis.org
1, 3, 15, 91, 613, 4410, 33190, 258129, 2058281, 16737259, 138268611, 1157197639, 9790774861, 83606543660, 719638883748, 6237175439640, 54386540912490, 476782443732437, 4199713449255749, 37151346765537606, 329914740292813170, 2939975733035070000
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, binomial(n+k, k)*binomial(4*n-k+2, n-4*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);
A368011
Expansion of (1/x) * Series_Reversion( x * ((1-x)^5-x^5) ).
Original entry on oeis.org
1, 5, 40, 385, 4095, 46377, 548380, 6691620, 83637450, 1065311665, 13777916774, 180451354720, 2388503030675, 31900445734050, 429369814375480, 5818270533841408, 79309912829992350, 1086768622818959100, 14961519902879613700, 206839961042385226110
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^5-x^5))/x)
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a(n) = sum(k=0, n\5, binomial(n+k, k)*binomial(6*n+4, n-5*k))/(n+1);
A369216
Expansion of (1/x) * Series_Reversion( x * ((1-x)^4-x) ).
Original entry on oeis.org
1, 5, 44, 479, 5827, 75887, 1034980, 14593794, 211031650, 3112385177, 46636714566, 707983562624, 10865572966703, 168306274609798, 2627854427929448, 41314461126179272, 653481096161664690, 10391753978329136808, 166040704868503173384
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serreverse(x*((1-x)^4-x))/x)
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a(n) = sum(k=0, n, binomial(n+k, k)*binomial(5*n+3*k+3, n-k))/(n+1);
Showing 1-6 of 6 results.