A068464 Factorial expansion of Gamma(1/4) = Sum_{n>=1} a(n)/n! with largest possible a(n), and Gamma = Euler's gamma function.

3, 1, 0, 3, 0, 0, 3, 0, 5, 3, 2, 7, 0, 2, 8, 9, 16, 3, 1, 15, 18, 8, 20, 7, 23, 8, 10, 11, 28, 29, 24, 30, 3, 16, 10, 8, 31, 11, 30, 35, 5, 5, 38, 32, 31, 42, 13, 17, 43, 3, 41, 27, 1, 14, 26, 52, 38, 22, 55, 46, 6, 35, 46, 34, 24, 52, 52, 64, 62, 25, 46, 56, 3, 71, 70, 22, 53, 63, 53

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for factorial base representation

Formula

a(n) = floor(n!*Gamma(1/4)) - n*floor((n-1)!*Gamma(1/4)), for n > 1. - M. F. Hasler, Nov 26 2018

Example

Gamma(1/4) = A068466 = 3.6256099... = 3/1! + 1/2! + 0 + 3/4! + 0 + 0 + 3/7! + 0 + 5/9! + 3/10! + 2/11! + ... - M. F. Hasler, Nov 26 2018

Mathematica

r:= Gamma[1/4]; Table[If[n == 1, Floor[r], Floor[n!*r]- n*Floor[(n-1)!*r] ], {n, 1, 100}] (* G. C. Greubel, Mar 29 2018 *)

Prog

(PARI) default(realprecision, 250); b = gamma(1/4); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", ")) \\ G. C. Greubel, Mar 29 2018
(PARI) A068464(N=90, c=gamma(precision(.25, logint(N!, 10)+1)))=vector(N, n, if(n>1, c=c%1*n, c)\1) \\ - M. F. Hasler, Nov 26 2018
(Magma) SetDefaultRealField(RealField(250));  [Floor(Gamma(1/4))] cat [Floor(Factorial(n)*Gamma(1/4)) - n*Floor(Factorial((n-1))*Gamma(1/4)) : n in [2..80]]; // G. C. Greubel, Nov 27 2018
(Sage)
def A068464(n):
    if (n==1): return floor(gamma(1/4))
    else: return expand(floor(factorial(n)*gamma(1/4)) - n*floor(factorial(n-1)*gamma(1/4)))
[A068464(n) for n in (1..80)] # G. C. Greubel, Nov 27 2018

Crossrefs

Cf. A007514, A068466 (decimal expansion), A068463.

Sequence in context: A355665 A144108 A163972 * A244679 A035674 A058600

Adjacent sequences: A068461 A068462 A068463 * A068465 A068466 A068467

Keyword

easy,nonn

Author

Benoit Cloitre, Mar 10 2002

Status

approved