A381882 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 * C(x)) ), where C(x) is the g.f. of A000108.

1, 4, 24, 175, 1428, 12525, 115468, 1103777, 10844715, 108860766, 1111722956, 11514401451, 120666441067, 1277161022725, 13633269293868, 146606818816257, 1586739194404521, 17271207134469417, 188942438655850740, 2076317084779878706, 22909617070555385010

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

G.f. A(x) satisfies A(x) = (1 + x*A(x))^3 * C(x*A(x)).

a(n) = Sum_{k=0..n} binomial(n+2*k+1,k) * binomial(3*n+3,n-k)/(n+2*k+1).

a(n) = binomial(3*(1 + n), n)*hypergeom([(1+n)/2, 1+n/2, -n], [2 + n, 4 + 2*n], -4)/(1 + n). - Stefano Spezia, Mar 09 2025

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3*(1-sqrt(1-4*x))/(2*x)))/x)

Crossrefs

Cf. A054727, A381881.

Cf. A000108, A381880.

Sequence in context: A347651 A032349 A215709 * A391677 A103334 A156017

Adjacent sequences: A381879 A381880 A381881 * A381883 A381884 A381885

Keyword

nonn

Author

Seiichi Manyama, Mar 09 2025

Status

approved