A369231
Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / (1-x+x^3)^2 ).
Original entry on oeis.org
1, 1, 2, 7, 26, 98, 385, 1569, 6556, 27908, 120624, 528030, 2336202, 10430155, 46930285, 212597901, 968833424, 4438398734, 20428750419, 94424634294, 438104297376, 2039690282940, 9526029685218, 44617396906698, 209526541600978, 986339358246758, 4653571637230839
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3/(1-x+x^3)^2)/x)
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a(n, s=3, 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);
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);
A372411
Coefficient of x^n in the expansion of ( (1-x+x^2)^2 / (1-x)^3 )^n.
Original entry on oeis.org
1, 1, 7, 34, 183, 1001, 5578, 31459, 179063, 1026493, 5918007, 34277728, 199309146, 1162682314, 6801575641, 39885002534, 234384591991, 1379936226605, 8137835460115, 48062073927739, 284233390132183, 1682950066882489, 9975692904121556, 59190095764321975
Offset: 0
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a(n, s=2, t=2, u=3) = sum(k=0, n\s, binomial(t*n, k)*binomial((u-t+1)*n-(s-1)*k-1, n-s*k));
Showing 1-3 of 3 results.