A359758 Expansion of 1/sqrt(1 - 4*x/(1-x)^5).
1, 2, 16, 110, 770, 5512, 40066, 294484, 2182850, 16288430, 122198926, 920820578, 6964483628, 52840433000, 401990254180, 3065365241440, 23422905551018, 179302895759782, 1374785979255880, 10556280995419090, 81161958814162700, 624750086745027388
Offset: 0
Keywords
Links
- Winston de Greef, Table of n, a(n) for n = 0..1110
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1-x)^5)) -
PARI
a(n)=sum(k=0, n, binomial(2*k,k) * binomial(n+4*k-1,n-k)) \\ Winston de Greef, Mar 24 2023
Formula
a(n) = Sum_{k=0..n} binomial(2*k,k) * binomial(n+4*k-1,n-k).
n*a(n) = (10*n-8)*a(n-1) - (19*n-46)*a(n-2) + 20*(n-3)*a(n-3) - 15*(n-4)*a(n-4) + 6*(n-5)*a(n-5) - (n-6)*a(n-6) for n > 5.
a(0) = 1; a(n) = (2/n) * Sum_{k=0..n-1} (n+k) * binomial(n+3-k,4) * a(k).
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