A369267
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, 5009, 29310, 175750, 1074264, 6668825, 41929970, 266464579, 1708829584, 11044663663, 71871779008, 470495357634, 3096311833496, 20472771422946, 135937759368388, 906056228361095, 6059922934991008, 40657629626645463
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)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
A369268
Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+x^3)^3 ).
Original entry on oeis.org
1, 1, 2, 8, 29, 105, 414, 1695, 7046, 29853, 128644, 561262, 2474142, 11006108, 49343508, 222715440, 1011217425, 4615519083, 21165513228, 97467424198, 450541090701, 2089777230606, 9723511785608, 45371996501895, 212271904284993, 995513843930049, 4679212044797252
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)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
A370248
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, 1200, 5293, 23427, 104425, 468428, 2110725, 9546256, 43315546, 197088195, 898910916, 4108495491, 18812770011, 86285313327, 396332663094, 1822878714492, 8394131895424, 38696042930251, 178561943852670, 824720550229584, 3812313399877776
Offset: 0
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a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*n, k)*binomial((u+1)*n-s*k-1, n-s*k));
Showing 1-3 of 3 results.