A369299
Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x^3)^3 ).
Original entry on oeis.org
1, 1, 2, 8, 29, 105, 417, 1719, 7181, 30603, 132736, 582790, 2585352, 11575613, 52237278, 237328704, 1084701387, 4983867447, 23007263941, 106658256768, 496336303014, 2317687534865, 10856677523580, 51001805706435, 240225121539000, 1134240896062656, 5367428039668751
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x^3)^3)/x)
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a(n, s=3, t=3, u=1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
A369298
Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x^3)^2 ).
Original entry on oeis.org
1, 2, 7, 32, 163, 884, 5011, 29342, 176092, 1077384, 6695093, 42140930, 268108170, 1721372836, 11138994028, 72573587520, 475674650717, 3134297846792, 20750020222815, 137953554890508, 920667400056250, 6165565645765092, 41419898169301995
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2*(1-x^3)^2)/x)
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a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
A369399
Expansion of (1/x) * Series_Reversion( x / (1+x) * (1-x^3)^2 ).
Original entry on oeis.org
1, 1, 1, 3, 11, 31, 86, 277, 937, 3095, 10275, 35091, 121662, 423286, 1481648, 5232315, 18601843, 66436069, 238327939, 858805613, 3106856141, 11277393837, 41062303214, 149948280259, 549027748390, 2015108865850, 7412690394406, 27324968423054
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x)*(1-x^3)^2)/x)
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a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial(u*(n+1), n-s*k))/(n+1);
A370274
Coefficient of x^n in the expansion of 1/( (1-x) * (1-x^3)^2 )^n.
Original entry on oeis.org
1, 1, 3, 16, 67, 276, 1212, 5391, 24003, 107719, 486728, 2208735, 10059868, 45970367, 210657177, 967636566, 4454109123, 20540731356, 94882599285, 438931979661, 2033217678792, 9429562243530, 43779688919145, 203463271733010, 946445226206940, 4406251540834026
Offset: 0
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a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((u+1)*n-s*k-1, n-s*k));
Showing 1-4 of 4 results.