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A361790
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Expansion of 1/sqrt(1 - 4*x/(1+x)^4).
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7
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1, 2, -2, -8, 6, 42, -8, -228, -90, 1210, 1238, -6116, -10864, 28574, 80932, -116248, -548010, 339678, 3455686, 173208, -20452674, -14036418, 113365140, 156407916, -580805472, -1312098918, 2659610562, 9621079540, -9902139124, -64566648122, 18521111032
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(2*k,k) * binomial(n+3*k-1,n-k).
n*a(n) = -( (n-3)*a(n-1) + (6*n-6)*a(n-2) + 10*(n-3)*a(n-3) + 5*(n-4)*a(n-4) + (n-5)*a(n-5) ) for n > 4.
a(0) = 1; a(n) = (2/n) * Sum_{k=0..n-1} (-1)^(n-1-k) * (n+k) * binomial(n+2-k,3) * a(k).
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PROG
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(PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1+x)^4))
(PARI) a(n)=sum(k=0, n, (-1)^(n-k) * binomial(2*k, k) * binomial(n+3*k-1, n-k)) \\ Winston de Greef, Mar 24 2023
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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