A368964
Expansion of (1/x) * Series_Reversion( x * (1-x-x^3)^3 ).
Original entry on oeis.org
1, 3, 15, 94, 660, 4959, 38995, 316875, 2639754, 22423292, 193484208, 1691190228, 14942632450, 133242614565, 1197520200870, 10836727044255, 98656011543816, 902936341411170, 8303218554134769, 76679352910367832, 710839322080978272, 6612557820697157410
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^3)^3)/x)
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a(n, s=3, t=3, u=0) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
A368971
Expansion of (1/x) * Series_Reversion( x * (1-x+x^2)^3 ).
Original entry on oeis.org
1, 3, 12, 52, 228, 969, 3795, 12285, 19227, -162316, -2334219, -20233746, -146642814, -956899038, -5761740810, -32172133140, -164988072288, -752632536117, -2777949390584, -5070274066512, 41416739288496, 663038498204040, 6188361199762260, 47738255512890555
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x+x^2)^3)/x)
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a(n, s=2, t=3, u=0) = sum(k=0, n\s, (-1)^k*binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
A370620
Coefficient of x^n in the expansion of 1 / (1-x-x^2)^(3*n).
Original entry on oeis.org
1, 3, 27, 255, 2535, 25908, 269667, 2843214, 30264975, 324543495, 3500669172, 37940361660, 412830243735, 4507040972190, 49345845670470, 541602648192480, 5957253066586815, 65650003858745514, 724693081872783375, 8011727857439155500, 88692087094226151300
Offset: 0
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a[n_]:=SeriesCoefficient[(1-x-x^2)^(-3*n),{x,0,n}]; Array[a,21,0] (* Stefano Spezia, May 01 2024 *)
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a(n, s=2, t=3, u=0) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t-u+1)*n-(s-1)*k-1, n-s*k));
A376326
Expansion of (1/x) * Series_Reversion( x * (1-x-x^2)^4 ).
Original entry on oeis.org
1, 4, 30, 272, 2737, 29380, 329614, 3818540, 45329440, 548511612, 6740687924, 83898110660, 1055441468145, 13398494365088, 171422870731600, 2208161418665872, 28614197357895055, 372754395074051500, 4878709294080115494, 64123505084010848580, 846018700129069313495
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^2)^4)/x)
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a(n, s=2, t=4, u=0) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
Showing 1-4 of 4 results.