A376791
Expansion of 1/sqrt((1 - x^3)^2 - 4*x).
Original entry on oeis.org
1, 2, 6, 21, 76, 282, 1065, 4074, 15732, 61193, 239406, 941064, 3713701, 14703896, 58383138, 232383841, 926943678, 3704410890, 14828984641, 59450138412, 238659074286, 959247218253, 3859777477944, 15546444564846, 62675854384977, 252893414725842, 1021208266423260
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(1/sqrt((1-x^3)^2-4*x))
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a(n) = sum(k=0, n\3, binomial(2*n-5*k, k)*binomial(2*n-6*k, n-3*k));
A376792
Expansion of 1/sqrt((1 - x^4)^2 - 4*x).
Original entry on oeis.org
1, 2, 6, 20, 71, 258, 954, 3572, 13501, 51404, 196858, 757472, 2926097, 11341032, 44080770, 171755976, 670664951, 2623732322, 10281616176, 40350944112, 158573538071, 623930435834, 2457658576132, 9690467310480, 38244489565051, 151064227161784, 597165099484632
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(1/sqrt((1-x^4)^2-4*x))
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a(n) = sum(k=0, n\4, binomial(2*n-7*k, k)*binomial(2*n-8*k, n-4*k));
A376810
Expansion of 1/sqrt(1 - 4*x/(1 - x^2)^2).
Original entry on oeis.org
1, 2, 6, 24, 94, 378, 1544, 6380, 26598, 111658, 471358, 1998924, 8509368, 36341278, 155634228, 668116136, 2874157222, 12387209982, 53475080494, 231189987224, 1000834283190, 4337864724462, 18821884379924, 81748960355484, 355383570351664, 1546239230878154
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1-x^2)^2))
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a(n) = sum(k=0, n\2, binomial(2*n-3*k-1, k)*binomial(2*n-4*k, n-2*k));
A383552
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) is the number of lattice paths from (0,0) to (n,k) using steps (1,0),(0,1),(2,2).
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 7, 4, 1, 1, 5, 12, 12, 5, 1, 1, 6, 18, 26, 18, 6, 1, 1, 7, 25, 47, 47, 25, 7, 1, 1, 8, 33, 76, 101, 76, 33, 8, 1, 1, 9, 42, 114, 189, 189, 114, 42, 9, 1, 1, 10, 52, 162, 321, 404, 321, 162, 52, 10, 1, 1, 11, 63, 221, 508, 772, 772, 508, 221, 63, 11, 1
Offset: 0
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, 7, ...
1, 3, 7, 12, 18, 25, 33, ...
1, 4, 12, 26, 47, 76, 114, ...
1, 5, 18, 47, 101, 189, 321, ...
1, 6, 25, 76, 189, 404, 772, ...
1, 7, 33, 114, 321, 772, 1645, ...
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a(n, k) = my(x='x+O('x^(n+1)), y='y+O('y^(k+1))); polcoef(polcoef(1/(1-x-y-x^2*y^2), n), k);
Showing 1-4 of 4 results.
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