A366082
Expansion of (1/x) * Series_Reversion( x*(1-x)^3/(1-x-x^2) ).
Original entry on oeis.org
1, 2, 6, 21, 79, 308, 1219, 4826, 18857, 71574, 257553, 837114, 2140496, 1379550, -35589730, -370646635, -2719034151, -17429175486, -103771133876, -588804389677, -3225403649859, -17180039158530, -89342552789741, -454604059204324, -2265246385921936
Offset: 0
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a(n) = sum(k=0, n\2, (-1)^k*binomial(n+1, k)*binomial(3*n-k+1, n-2*k))/(n+1);
A369229
Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / (1-x+x^2)^2 ).
Original entry on oeis.org
1, 1, 4, 15, 65, 298, 1429, 7073, 35869, 185403, 973198, 5173644, 27797914, 150715321, 823541564, 4530609391, 25073291597, 139492998775, 779706274423, 4376600956063, 24659875131049, 139424357994344, 790763858547445, 4497788153203946, 25650342635871106
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3/(1-x+x^2)^2)/x)
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a(n, s=2, t=2, u=3) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u-t+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
A366050
Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1-x+x^2) ).
Original entry on oeis.org
1, 3, 16, 104, 750, 5769, 46373, 384885, 3273118, 28372354, 249762585, 2226782078, 20065651123, 182457467898, 1672073116401, 15427427247088, 143191280370438, 1336062703751262, 12524930325385008, 117910257665608080, 1114233543986585741
Offset: 0
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a(n) = sum(k=0, n\2, binomial(n+1, k)*binomial(4*n-k+2, n-2*k))/(n+1);
A369230
Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / (1-x+x^2)^3 ).
Original entry on oeis.org
1, 0, 3, 3, 24, 54, 283, 900, 4098, 15286, 66555, 268173, 1156951, 4852722, 21007605, 90167059, 393152058, 1712432070, 7524092134, 33112353060, 146518404963, 649861681966, 2893369443183, 12913307575722, 57800647230933, 259298148600504, 1165967972216967
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3/(1-x+x^2)^3)/x)
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a(n, s=2, t=3, u=3) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u-t+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
A372410
Coefficient of x^n in the expansion of ( (1-x+x^2) / (1-x)^3 )^n.
Original entry on oeis.org
1, 2, 12, 77, 516, 3552, 24891, 176647, 1265508, 9132530, 66288762, 483442434, 3539626635, 26002266656, 191556630375, 1414649524077, 10469628711396, 77630719516650, 576585458828844, 4288881479411395, 31945446999811266, 238233164413294792, 1778587750475510316
Offset: 0
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a(n, s=2, t=1, u=3) = sum(k=0, n\s, binomial(t*n, k)*binomial((u-t+1)*n-(s-1)*k-1, n-s*k));
Showing 1-5 of 5 results.