A381820 Expansion of ( (1/x) * Series_Reversion( x * ((1-x) / C(x))^4 ) )^(1/4), where C(x) is the g.f. of A000108.

1, 2, 20, 281, 4599, 82113, 1550993, 30473930, 616463800, 12753523628, 268586285058, 5738804673016, 124098812744140, 2710824280371114, 59728504549831296, 1325862161472193292, 29623682752417138511, 665679666998856945540, 15034747192791290846435

Offset: 0

Author

Seiichi Manyama, Mar 07 2025

Keywords

• nonn

Crossrefs

Cf. A381817, A381818, A381819.

Cf. A000108, A381774.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec((serreverse(x*((1-x)*2*x/(1-sqrt(1-4*x)))^4)/x)^(1/4))

Formula

G.f. A(x) satisfies A(x) = C(x*A(x)^4) / (1 - x*A(x)^4).

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