A369125
Expansion of (1/x) * Series_Reversion( x * ((1-x)^5+x^5) ).
Original entry on oeis.org
1, 5, 40, 385, 4095, 46375, 548300, 6689550, 83593250, 1064463125, 13762667750, 180189122750, 2384130651875, 31829162793750, 428227113655000, 5800188020157500, 79026653220693750, 1082367047392625000, 14893567523068062500, 205796463286063912500
Offset: 0
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A369125 := proc(n)
add((-1)^k * binomial(n+k,k) * binomial(6*n+4,n-5*k),k=0..floor(n/5)) ;
%/(n+1) ;
end proc;
seq(A369125(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)^5+x^5))/x)
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a(n) = sum(k=0, n\5, (-1)^k*binomial(n+k, k)*binomial(6*n+4, n-5*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);
A369123
Expansion of (1/x) * Series_Reversion( x * ((1-x)^2+x^2) ).
Original entry on oeis.org
1, 2, 6, 20, 68, 224, 672, 1584, 880, -22880, -215072, -1414400, -8012032, -41344000, -198120448, -884348160, -3640426752, -13403384320, -40424947200, -65476561920, 329862128640, 4603911045120, 35276325027840, 221747978649600, 1244854463643648
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^2+x^2))/x)
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a(n) = sum(k=0, n\2, (-1)^k*binomial(n+k, k)*binomial(3*n+1, n-2*k))/(n+1);
A371432
Expansion of (1/x) * Series_Reversion( x * ((1-x)^2 + x^4) ).
Original entry on oeis.org
1, 2, 7, 30, 142, 714, 3740, 20178, 111325, 625042, 3559101, 20502014, 119249277, 699330360, 4130235408, 24543145310, 146629131642, 880184547880, 5305961255490, 32107022363150, 194947974895960, 1187354222296110, 7252099548616320, 44408257163905050
Offset: 0
-
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, (-1)^k*binomial(n+k, k)*binomial(3*n-2*k+1, n-4*k))/(n+1);
A371436
Expansion of (1/x) * Series_Reversion( x * ((1-x)^4 + x) ).
Original entry on oeis.org
1, 3, 12, 49, 179, 441, -860, -23634, -229246, -1705649, -10757370, -57800600, -246084657, -551185526, 3612960360, 66196180728, 641858169138, 4911870929096, 31792139997384, 172691510260794, 711428107177975, 1066704835555530, -18659356513414560
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^4+x))/x)
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a(n) = sum(k=0, n, (-1)^k*binomial(n+k, k)*binomial(5*n+3*k+3, n-k))/(n+1);
Showing 1-5 of 5 results.