A393380 Expansion of (1/x) * Series_Reversion( x * (2/(1 + x)^3 - 1) ).

1, 6, 60, 740, 10194, 150318, 2321096, 37053792, 606606090, 10128418982, 171815202132, 2952836422068, 51303782749002, 899655115793310, 15902112961281552, 283029984745521568, 5068033002913297266, 91236932904020112774, 1650331838235907956140, 29979618733313935858788

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

G.f. A(x) satisfies A(x) = 1/(2/(1 + x*A(x))^3 - 1).

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

Prog

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

Crossrefs

Cf. A006318, A228966.

Sequence in context: A000894 A112117 A065944 * A357771 A392645 A126779

Adjacent sequences: A393377 A393378 A393379 * A393381 A393382 A393383

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2026

Status

approved