A182480 Decimal expansion of 16000000/63.

2, 5, 3, 9, 6, 8, 2, 5, 3, 9, 6, 8, 2, 5, 3, 9, 6, 8, 2, 5, 3, 9, 6, 8, 2, 5, 3, 9, 6, 8, 2, 5, 3, 9, 6, 8, 2, 5, 3, 9, 6, 8, 2, 5, 3, 9, 6, 8, 2, 5, 3, 9, 6, 8, 2, 5, 3, 9, 6, 8, 2, 5, 3, 9, 6, 8, 2, 5, 3, 9, 6, 8, 2, 5, 3, 9, 6, 8, 2, 5, 3, 9, 6, 8, 2, 5, 3

Offset

6,1

Comments

The negative case of this sequence, viz. -253968.253968253968... may be derived from a formula from Hardy & Wright in a proof of the irrationality of e. See also A021256, the decimal expansion of 1/252, the negative case of which is zeta(-5), the Riemann zeta function.

Also, continued fraction expansion of (7672+sqrt(73650723))/7429. [Bruno Berselli, May 02 2012]

References

Hardy & Wright, An Introduction to the Theory of Numbers, Oxford, Sixth Ed. 2008, p.53.

Links

Vincenzo Librandi, Table of n, a(n) for n = 6..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).

Formula

G.f.: x^6*(2+3*x-2*x^2+8*x^3)/(1-x+x^3-x^4). [Bruno Berselli, May 02 2012]

a(n) = (1/30)*(41*(n mod 6)+((n+1) mod 6)+26*((n+2) mod 6)-19*((n+3) mod 6)+21*((n+4) mod 6)-4*((n+5) mod 6)). [Bruno Berselli, May 02 2012]

a(n) = a(n-1)-a(n-3)+a(n-4). - Vincenzo Librandi, Jun 14 2013

Example

For X=5, n=7 the solution of (X^n * (1-X)^n)/n! is -253968.253968253968253968253968253968253968....

Mathematica

RealDigits[16000000/63, 10, 105][[1]] (* Bruno Berselli, May 02 2012 *)
CoefficientList[Series[(2 + 3 x - 2 x^2 + 8 x^3) / (1 - x + x^3 - x^4), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 14 2013 *)
PadRight[{}, 120, {2, 5, 3, 9, 6, 8}] (* or *) LinearRecurrence[{1, 0, -1, 1}, {2, 5, 3, 9}, 20] (* Harvey P. Dale, Jul 02 2016 *)

Prog

User RPL (for the HP50g)  << -> x n << x n ^ 1 x - n ^ * n ! / ->NUM >> >>
(Magma)  I:=[2, 5, 3, 9]; [n le 4 select I[n] else Self(n-1)-Self(n-3)+Self(n-4): n in [1..80]]; // Vincenzo Librandi, Jun 14 2013

Crossrefs

Apart from first 2 digits the same as A021256.

Sequence in context: A122281 A363677 A340927 * A193974 A319499 A318578

Adjacent sequences: A182477 A182478 A182479 * A182481 A182482 A182483

Keyword

nonn,cons,easy

Author

Douglas L. Fox, May 01 2012

Status

approved