A369265
Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / (1+x^3) ).
Original entry on oeis.org
1, 2, 7, 31, 153, 806, 4439, 25250, 147193, 874732, 5279635, 32276245, 199439761, 1243633652, 7815804351, 49455190791, 314807497953, 2014530780524, 12952334769203, 83628832755779, 542022781854953, 3525150296312984, 22998642171764363, 150478455899387966
Offset: 0
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A369265 := proc(n)
add(binomial(n+1,k) * binomial(3*n-3*k+1,n-3*k),k=0..floor(n/3)) ;
%/(n+1) ;
end proc;
seq(A369265(n),n=0..70) ; # R. J. Mathar, Jan 25 2024
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2/(1+x^3))/x)
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a(n, s=3, t=1, 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);
A369300
Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x^3)^3 ).
Original entry on oeis.org
1, 2, 7, 33, 173, 962, 5589, 33546, 206359, 1294096, 8242375, 53173095, 346724250, 2281555440, 15131448440, 101038950441, 678724811604, 4583483218340, 31098830566098, 211898222878937, 1449322361547669, 9947227335902244, 68486384818253877
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2*(1-x^3)^3)/x)
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a(n, s=3, t=3, 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);
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);
A369270
Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / (1+x^3)^3 ).
Original entry on oeis.org
1, 3, 15, 94, 657, 4902, 38233, 307953, 2541831, 21386810, 182754162, 1581699162, 13836248406, 122139271098, 1086638457429, 9733419373534, 87707244737511, 794505072627735, 7231017033165776, 66089527981542462, 606340568510978940, 5582088822346925210
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+1)*(n+1)-s*k-2, n-s*k))/(n+1);
Showing 1-5 of 5 results.