A393420 Expansion of (1/x) * Series_Reversion( x * (4 * (1 - x)^2 - 3) ).

1, 8, 124, 2400, 52016, 1207808, 29379840, 739014144, 19065460480, 501694482432, 13413481036800, 363345251303424, 9950454941564928, 275038274134999040, 7663078706655395840, 214990114377881223168, 6068314538667340136448, 172205110768067713433600, 4910172479006050281062400

Offset

0,2

Links

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

Formula

G.f. A(x) satisfies A(x) = 1/(4 * (1 - x*A(x))^2 - 3).

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

D-finite with recurrence 3*n*(n+1)*a(n) -46*n*(2*n-1)*a(n-1) -3*(3*n-2)*(3*n-4)*a(n-2)=0. - R. J. Mathar, Feb 24 2026

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(4*(1-x)^2-3))/x)

Crossrefs

Cf. A006013, A393418, A393419, A393421.

Sequence in context: A120957 A302356 A367122 * A069459 A254125 A371298

Adjacent sequences: A393417 A393418 A393419 * A393421 A393422 A393423

Keyword

nonn

Author

Seiichi Manyama, Feb 14 2026

Status

approved