A235348 Series reversion of x*(1-2*x-5*x^2)/(1-x^2).

1, 2, 12, 82, 636, 5266, 45684, 409706, 3768132, 35346082, 336854844, 3252391170, 31746462732, 312755404818, 3105750620772, 31054695744570, 312404601250644, 3159598296022978, 32108181705850860, 327682918265502002, 3357089384702757276

Offset: 1

Author

Fung Lam, Jan 13 2014

Keywords

• nonn
• easy

Comments

Sum of turbulence series A107841 and A235347.

Links

• Fung Lam, Table of n, a(n) for n = 1..1000

Programs

Mathematica

Rest[CoefficientList[InverseSeries[Series[x*(1-2*x-5*x^2)/(1-x^2), {x, 0, 20}], x],x]] (* Vaclav Kotesovec, Jan 29 2014 *)

PARI

Vec( serreverse(x*(1-2*x-5*x^2)/(1-x^2) +O(x^66) ) ) \\ Joerg Arndt, Jan 14 2014

Python

# R. J. Mathar, 2023-03-28
class A235348() :
    def _init_(self) :
        self.a = [1, 2, 12, 82, 636, 5266]
    def at(self, n):
        if n <= len(self.a):
            return self.a[n-1]
        else:
            rhs = -3*(n-1)*(160*n-237)*self.at(n-1) \
            +3*(-422*n**2+1721*n-1713)*self.at(n-2) \
            +2*(-67*n**2+388*n-552)*self.at(n-3) \
            +(137*n**2-1352*n+3279)*self.at(n-4) \
            +(7*n-37)*(n-6)*self.at(n-5) -(n-6)*(n-7)*self.at(n-6)
            rhs //= (-54*n*(n-1))
            self.a.append(rhs)
            return self.a[-1]
a235348 = A235348()
for n in range(1,12):
    print(a235348.at(n))
# a235348.

Formula

D-finite with recurrence 54*n*(n-1)*a(n) -3*(n-1)*(160*n-237)*a(n-1) +3*(-422*n^2+1721*n-1713)*a(n-2) +2*(-67*n^2+388*n-552)*a(n-3) +(137*n^2-1352*n+3279)*a(n-4) +(7*n-37)*(n-6)*a(n-5) -(n-6)*(n-7)*a(n-6)=0. - R. J. Mathar, Mar 24 2023