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Expansion of 1/sqrt(1 - 4*x/(1-x)^6).
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%I #21 Mar 28 2023 14:01:26

%S 1,2,18,134,1010,7788,60978,482708,3853338,30964238,250150176,

%T 2029781310,16530857930,135051216620,1106287906140,9083459084364,

%U 74734798117570,615998603183550,5085522355488150,42045309424052250,348067638153560040,2884832348569699340

%N Expansion of 1/sqrt(1 - 4*x/(1-x)^6).

%F a(n) = Sum_{k=0..n} binomial(2*k,k) * binomial(n+5*k-1,n-k).

%F 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.

%F a(0) = 1; a(n) = (2/n) * Sum_{k=0..n-1} (n+k) * binomial(n+4-k,5) * a(k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1-x)^6))

%Y Cf. A085362, A110170, A162478, A359489, A359758.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 24 2023