A361844
Expansion of 1/(1 - 9*x*(1-x)^2)^(1/3).
Original entry on oeis.org
1, 3, 12, 57, 297, 1629, 9216, 53217, 311796, 1846818, 11032416, 66356712, 401364531, 2439135585, 14882263002, 91116281565, 559528781697, 3445002647847, 21260140172244, 131474746842345, 814564464082263, 5055177167348463, 31420067723814780
Offset: 0
-
A361844 := n -> (-9)^n*binomial(-1/3, n)*hypergeom([1/3 - n*2/3, 2/3 - n*2/3,
-n*2/3], [1/2 - n, 2/3 - n], 3/4):
seq(simplify(A361844(n)), n = 0..22); # Peter Luschny, Mar 27 2023
-
my(N=30, x='x+O('x^N)); Vec(1/(1-9*x*(1-x)^2)^(1/3))
A361816
Expansion of 1/sqrt(1 - 4*x*(1-x)^3).
Original entry on oeis.org
1, 2, 0, -10, -22, 12, 174, 344, -354, -3304, -5780, 9180, 65258, 99132, -226620, -1313580, -1690990, 5441340, 26681700, 28070100, -128211552, -543818824, -440381780, 2978145240, 11080939914, 6162798092, -68377892976, -225107280388, -64286124152
Offset: 0
A361834
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} (-1)^(n-j) * binomial(2*j,j) * binomial(k*j,n-j).
Original entry on oeis.org
1, 1, 2, 1, 2, 6, 1, 2, 4, 20, 1, 2, 2, 8, 70, 1, 2, 0, -2, 16, 252, 1, 2, -2, -10, -14, 32, 924, 1, 2, -4, -16, -22, -32, 64, 3432, 1, 2, -6, -20, -10, 12, -30, 128, 12870, 1, 2, -8, -22, 20, 118, 174, 64, 256, 48620, 1, 2, -10, -22, 66, 242, 304, 344, 346, 512, 184756
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
2, 2, 2, 2, 2, 2, 2, ...
6, 4, 2, 0, -2, -4, -6, ...
20, 8, -2, -10, -16, -20, -22, ...
70, 16, -14, -22, -10, 20, 66, ...
252, 32, -32, 12, 118, 242, 342, ...
924, 64, -30, 174, 304, 82, -678, ...
-
T(n, k) = sum(j=0, n, (-1)^(n-j)*binomial(2*j, j)*binomial(k*j, n-j));
A361817
Expansion of 1/sqrt(1 - 4*x*(1-x)^4).
Original entry on oeis.org
1, 2, -2, -16, -10, 118, 304, -500, -3754, -2488, 30866, 83716, -135568, -1080972, -792876, 9090484, 25788118, -39325156, -335074520, -271779024, 2820643842, 8348113120, -11788972644, -107836934448, -96107852032, 900943403012, 2778574561276, -3596374190416
Offset: 0
Showing 1-4 of 4 results.