A371987 G.f. A(x) satisfies A(x) = ( 1 + 9*x*(1 + A(x)) )^(1/3).

1, 6, -18, 90, -486, 2430, -8586, -17982, 841266, -12165066, 136875582, -1348875990, 12016318410, -96794708562, 685263211974, -3870181566702, 10180063779426, 147487856352102, -3442575733736562, 47851939835741178, -546779680526987910, 5515345957243519710

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = 9^n * Sum_{k=0..n} binomial(n,k) * binomial(k/3+1/3,n)/(k+1).

G.f.: (6*2^(1/3)*x + 2^(2/3) * (1 + 9*x + sqrt(1+9*x*(2+3*(3-4*x)*x)))^(2/3)) / (2*(1 + 9*x + sqrt(1+9*x*(2+3*(3-4*x)*x)))^(1/3)). - Vaclav Kotesovec, Apr 15 2024

Mathematica

CoefficientList[Series[(6*2^(1/3)*x + 2^(2/3)*(1 + 9*x + Sqrt[1 + 9*x*(2 + 3*(3 - 4*x)*x)])^(2/3))/(2*(1 + 9*x + Sqrt[1 + 9*x*(2 + 3*(3 - 4*x)*x)])^(1/3)), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 15 2024 *)

Prog

(PARI) a(n) = 9^n*sum(k=0, n, binomial(n, k)*binomial(k/3+1/3, n)/(k+1));

Crossrefs

Cf. A371988.

Sequence in context: A219590 A260664 A279260 * A294471 A194995 A104970

Adjacent sequences: A371984 A371985 A371986 * A371988 A371989 A371990

Keyword

sign

Author

Seiichi Manyama, Apr 15 2024

Status

approved