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

Author

Benoit Cloitre, Mar 10 2002

Keywords

• easy
• nonn

Examples

			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
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for factorial base representation

Crossrefs

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

Programs

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

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 *)

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

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

Formula

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