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));
A370621
Coefficient of x^n in the expansion of ( (1-x) / (1-x-x^2)^3 )^n.
Original entry on oeis.org
1, 2, 16, 119, 948, 7732, 64231, 540311, 4588076, 39244106, 337624066, 2918384229, 25325306031, 220497804256, 1925231880973, 16850975055139, 147807248526268, 1298926641563548, 11434042768577866, 100800817171002817, 889839745865544598
Offset: 0
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a[n_]:=SeriesCoefficient[((1-x)/(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=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t-u+1)*n-(s-1)*k-1, n-s*k));
A370622
Coefficient of x^n in the expansion of ( (1-x)^2 / (1-x-x^2)^3 )^n.
Original entry on oeis.org
1, 1, 9, 46, 293, 1806, 11538, 74173, 482157, 3154645, 20762014, 137270376, 911111522, 6067104434, 40514133081, 271195540971, 1819188150365, 12225956834430, 82301499780885, 554850642658483, 3745615502285478, 25315915432984852, 171292993893095996
Offset: 0
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a[n_]:=SeriesCoefficient[((1-x)^2/(1-x-x^2)^3)^n,{x,0,n}]; Array[a,23,0] (* Stefano Spezia, May 01 2024 *)
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a(n, s=2, t=3, u=2) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t-u+1)*n-(s-1)*k-1, n-s*k));
Showing 1-3 of 3 results.