A206531 -id:A206531 - cp's OEIS frontend

A206532 a(n) = (2(n+1)(2n+1)-1) * a(n-1) + 2n(2n-1) * a(n-2), a(0) = 1, a(1) = 11.

1, 11, 331, 18535, 1668151, 220195931, 40075659443, 9618158266319, 2943156429493615, 1118399443207573699, 516700542761899048939, 285218699604568275014327, 185392154742969378759312551, 140156468985684850342040288555

Offset: 0

Seiichi Kirikami, Feb 11 2012

nonn

The denominators of the fractions limiting to the value of A206533.

E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, Inc.,1966.

Robert Israel, Table of n, a(n) for n = 0..223

Cf. A002939, A082108, A206531, A206533.

f:= gfun:-rectoproc({a(n) = (2*(n+1)*(2*n+1)-1) * a(n-1) + 2*n*(2*n-1) * a(n-2), a(0) = 1, a(1) = 11},a(n),remember):
map(f, [$0..40]); # Robert Israel, Sep 16 2018

RecurrenceTable[{a[n]==(2(n+1)(2n+1)-1)a[n-1]+2n(2n-1)a[n-2],a[0]==1,a[1]==11},a,{n,15}]

a(n) = A082108*a(n-1) + A002939*a(n-2), a(0) = 1, a(1) = 11.

a(n) = -4*n*(-1)^n*(n+1)*LommelS1(2*n+1/2, 3/2, 1)-2*(-1)^n*(n+1)*LommelS1(2*n+3/2, 1/2, 1)+(1-cos(1))*(2*n+2)!+(-1)^n. - Robert Israel, Sep 16 2018

A206533 Decimal expansion of 1/(1-cos(1)).

Original entry on oeis.org

2, 1, 7, 5, 3, 4, 2, 6, 4, 9, 6, 7, 0, 0, 2, 1, 4, 1, 0, 7, 7, 6, 7, 8, 6, 7, 5, 9, 6, 5, 6, 0, 6, 9, 9, 7, 5, 8, 4, 8, 4, 4, 7, 4, 6, 7, 6, 2, 4, 1, 8, 4, 2, 1, 3, 7, 5, 0, 5, 4, 0, 0, 5, 5, 1, 4, 7, 0, 3, 0, 7, 1, 0, 2, 8, 9, 3, 5, 0, 6, 1, 8, 1, 9, 9, 0, 8, 7, 8, 4, 0, 4, 8, 3, 5, 5, 8, 2, 9, 1, 0, 8

Offset: 1

Seiichi Kirikami, Feb 11 2012

The value of the fractional limit of the numerators(A206531+2*A206532) and the denominators(A206532).

Abs(A206532/(1-cos(1)) - (A206531+2*A206532)) -> 0.

			2.17534264967002141077678675965606997584844...

E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, Inc., 1966.

Cf. A002939, A082108, A206531, A206532, A049470, A371936.

Mathematica
```
RealDigits[N[1/(1-Cos[1]), 150]][[1]]
```

1/(1 - cos(1)) \\ Stefano Spezia, Apr 21 2025

Equals 1/(1-A049470).
A206531/A206532+2 -> 1/(1-A049470).
Equals 1/A371936. - Hugo Pfoertner, Apr 21 2025

Incorrect a(86)=9 removed by Georg Fischer, Apr 04 2020

cp's OEIS Frontend

A206532 a(n) = (2(n+1)(2n+1)-1) * a(n-1) + 2n(2n-1) * a(n-2), a(0) = 1, a(1) = 11.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Maple

Mathematica

Formula