A369441
Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x^2)^2) ).
Original entry on oeis.org
1, 2, 7, 30, 141, 704, 3666, 19686, 108222, 606062, 3445308, 19829680, 115323955, 676659960, 4000719012, 23811922678, 142557391306, 857894530348, 5186614665121, 31487226410770, 191871141682557, 1173163962971056, 7195329233469552, 44255915928488880
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+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(u*(n+1), n-s*k))/(n+1);
A369477
Expansion of (1/x) * Series_Reversion( x / ((1+x) * (1+x+x^2)^2) ).
Original entry on oeis.org
1, 3, 14, 77, 464, 2964, 19717, 135131, 947549, 6765642, 49022225, 359545750, 2664127354, 19913283809, 149968276974, 1136856855549, 8668000962927, 66428474900907, 511414514214628, 3953420853213504, 30674783555852576, 238808419235022293, 1864869207177530320
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+x+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((t+u)*(n+1)-k, n-s*k))/(n+1);
A370194
Coefficient of x^n in the expansion of ( (1+x) * (1+x^2)^2 )^n.
Original entry on oeis.org
1, 1, 5, 19, 77, 326, 1391, 6028, 26349, 116011, 513730, 2285570, 10208111, 45742724, 205550840, 925918544, 4179740909, 18903381337, 85635147983, 388517336189, 1765019420602, 8028115465732, 36555667019338, 166621503161184, 760161934681647, 3470945792364701
Offset: 0
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a[n_]:=SeriesCoefficient[((1+x)*(1+x^2)^2)^n,{x,0,n}]; Array[a,26,0] (* Stefano Spezia, Apr 30 2024 *)
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a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*n, k)*binomial(u*n, n-s*k));
Showing 1-3 of 3 results.