A360132 Expansion of 1/sqrt(1 - 4*x/(1-x)^6).
1, 2, 18, 134, 1010, 7788, 60978, 482708, 3853338, 30964238, 250150176, 2029781310, 16530857930, 135051216620, 1106287906140, 9083459084364, 74734798117570, 615998603183550, 5085522355488150, 42045309424052250, 348067638153560040, 2884832348569699340
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1-x)^6))
Formula
a(n) = Sum_{k=0..n} binomial(2*k,k) * binomial(n+5*k-1,n-k).
n*a(n) = (11*n-9)*a(n-1) - (25*n-60)*a(n-2) + 35*(n-3)*a(n-3) - 35*(n-4)*a(n-4) + 21*(n-5)*a(n-5) - 7*(n-6)*a(n-6) + (n-7)*a(n-7) for n > 6.
a(0) = 1; a(n) = (2/n) * Sum_{k=0..n-1} (n+k) * binomial(n+4-k,5) * a(k).