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);
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);
A369398
Expansion of (1/x) * Series_Reversion( x / (1+x)^2 * (1-x^3) ).
Original entry on oeis.org
1, 2, 5, 15, 52, 198, 797, 3322, 14195, 61848, 273792, 1228131, 5570200, 25501610, 117694557, 546983631, 2557677780, 12024345942, 56801925455, 269483935384, 1283469626512, 6134259516564, 29412031039568, 141434223863670, 681939435678239, 3296147009539144
Offset: 0
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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-1, k)*binomial(u*(n+1), n-s*k))/(n+1);
A370273
Coefficient of x^n in the expansion of 1/( (1-x)^2 * (1-x^3) )^n.
Original entry on oeis.org
1, 2, 10, 59, 362, 2277, 14581, 94572, 619242, 4084538, 27099435, 180651913, 1209036725, 8118629365, 54671662692, 369071775684, 2496852123882, 16923762715911, 114902801532622, 781296976824693, 5319705042364587, 36265061394634215, 247497082392976415
Offset: 0
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a(n, s=3, t=1, u=2) = 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.