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A361816
Expansion of 1/sqrt(1 - 4*x*(1-x)^3).
5
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
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(2*k,k) * binomial(3*k,n-k).
n*a(n) = 2 * ( (2*n-1)*a(n-1) - 3*(2*n-2)*a(n-2) + 3*(2*n-3)*a(n-3) - (2*n-4)*a(n-4) ) for n > 3.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x*(1-x)^3))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Mar 25 2023
STATUS
approved