A369440
Expansion of (1/x) * Series_Reversion( x / ((1+x) * (1+x^2)^2) ).
Original entry on oeis.org
1, 1, 3, 9, 30, 107, 396, 1513, 5915, 23554, 95202, 389555, 1610588, 6717816, 28234064, 119452553, 508330809, 2174393331, 9343913933, 40319400738, 174630125428, 758916134002, 3308320668768, 14462616815619, 63388694309005, 278492994845776, 1226241871745376
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+x^2)^2))/x)
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a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial(u*(n+1), n-s*k))/(n+1);
A369478
Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x+x^2)^2) ).
Original entry on oeis.org
1, 4, 24, 170, 1320, 10868, 93197, 823484, 7445184, 68545882, 640446224, 6057249180, 57878746750, 557903174040, 5418441862824, 52971933934834, 520869559359424, 5147999004530720, 51113415228327827, 509583784051748692, 5099262428810825568
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+x+x^2)^2))/x)
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a(n, s=2, t=2, u=2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
A370195
Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x^2)^2 )^n.
Original entry on oeis.org
1, 2, 10, 56, 322, 1902, 11440, 69680, 428418, 2653292, 16527910, 103443144, 649964176, 4097464490, 25904239560, 164168677056, 1042651014018, 6634470805556, 42286359318364, 269925368946896, 1725325033144622, 11041442722096094, 70739175615642016
Offset: 0
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a[n_]:=SeriesCoefficient[((1+x)^2*(1+x^2)^2)^n,{x,0,n}]; Array[a,23,0] (* Stefano Spezia, Apr 30 2024 *)
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a(n, s=2, t=2, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial(u*n, n-s*k));
A369594
Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 * (1+x^3)^3) ).
Original entry on oeis.org
1, 3, 12, 58, 318, 1887, 11772, 75969, 502554, 3389056, 23211312, 161015058, 1128976523, 7988381001, 56968671948, 409046328954, 2954644519365, 21455293440345, 156534285598068, 1146881543952792, 8434926025730955, 62250461094154372, 460859182211975184
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3*(1+x^3)^3))/x)
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a(n, s=3, t=3, u=3) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial(u*(n+1), n-s*k))/(n+1);
Showing 1-4 of 4 results.