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);
A369296
Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x^3)^2 ).
Original entry on oeis.org
1, 1, 2, 7, 24, 84, 315, 1225, 4859, 19646, 80739, 336050, 1413587, 6000777, 25674462, 110598855, 479286932, 2088036939, 9139604421, 40174594432, 177267942918, 784889441217, 3486198469890, 15529021825140, 69355660644738, 310509670642611, 1393296782758244
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+1)*(n+1)-s*k-2, n-s*k))/(n+1);
A369297
Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x^3) ).
Original entry on oeis.org
1, 2, 7, 31, 153, 806, 4440, 25266, 147364, 876282, 5292527, 32378125, 200218715, 1249456536, 7858638756, 49766595855, 317051378103, 2030589300596, 13066646029059, 84439101344619, 547746622599561, 3565472378360110, 23282050305073680, 152466688160732190
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+1)*(n+1)-s*k-2, n-s*k))/(n+1);
A366041
Expansion of (1/x) * Series_Reversion( x*(1-x)*(1-x^4) ).
Original entry on oeis.org
1, 1, 2, 5, 15, 48, 160, 549, 1930, 6919, 25200, 92976, 346757, 1305140, 4951216, 18912245, 72675114, 280761670, 1089800270, 4248149795, 16623209911, 65273370720, 257115465600, 1015719256200, 4023178881540, 15974388769653, 63570826294760
Offset: 0
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a(n) = sum(k=0, n\4, binomial(n+k, n)*binomial(2*n-4*k, n))/(n+1);
A366042
Expansion of (1/x) * Series_Reversion( x*(1-x)*(1-x^5) ).
Original entry on oeis.org
1, 1, 2, 5, 14, 43, 139, 465, 1595, 5577, 19805, 71240, 259037, 950590, 3516110, 13095440, 49068051, 184839543, 699607625, 2659276675, 10147039881, 38853068780, 149240187330, 574913637375, 2220609902199, 8598120578442, 33366877654697, 129758691426484
Offset: 0
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a(n) = sum(k=0, n\5, binomial(n+k, n)*binomial(2*n-5*k, n))/(n+1);
A370272
Coefficient of x^n in the expansion of 1/( (1-x) * (1-x^3) )^n.
Original entry on oeis.org
1, 1, 3, 13, 51, 201, 819, 3382, 14067, 58927, 248303, 1051128, 4466787, 19043766, 81418746, 348936288, 1498601459, 6448162221, 27791057997, 119954739879, 518451715551, 2243481128020, 9718784202240, 42143960004750, 182917942802595, 794589638379576
Offset: 0
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a(n, s=3, t=1, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((u+1)*n-s*k-1, n-s*k));
Showing 1-6 of 6 results.