A361813 Expansion of 1/sqrt(1 - 4*x*(1+x)^4).

1, 2, 14, 80, 486, 3030, 19184, 122924, 794678, 5173160, 33863666, 222683588, 1469908848, 9733916596, 64636957300, 430240178484, 2869778018070, 19177245746844, 128361805431752, 860443079597872, 5775392952659170, 38811408514848032, 261101034656317244

Offset: 0

Author

Seiichi Manyama, Mar 25 2023

Keywords

• nonn

Crossrefs

Cf. A006139, A137635, A360133, A361790, A361791, A361792, A361812, A361814.

Programs

PARI

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

Formula

a(n) = Sum_{k=0..n} binomial(2*k,k) * binomial(4*k,n-k).

n*a(n) = 2 * ( (2*n-1)*a(n-1) + 4*(2*n-2)*a(n-2) + 6*(2*n-3)*a(n-3) + 4*(2*n-4)*a(n-4) + (2*n-5)*a(n-5) ) for n > 4.