A381774 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, 19, 255, 3995, 68344, 1237526, 23316295, 452385355, 8977539540, 181374792040, 3718002102747, 77138798530854, 1616741658725930, 34179703551312530, 728019711835819493, 15608122038151106507, 336551042553481867640, 7293934071668996347055

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

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

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

Prog

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

Crossrefs

Cf. A054727, A060941, A381772, A381773, A381775.

Cf. A000108.

Sequence in context: A234505 A239108 A191806 * A349721 A379287 A252710

Adjacent sequences: A381771 A381772 A381773 * A381775 A381776 A381777

Keyword

nonn

Author

Seiichi Manyama, Mar 07 2025

Status

approved