A068463 Factorial expansion of Gamma(3/4) = Sum_{n>=1} a(n)/n! where Gamma is Euler's gamma function.

1, 0, 1, 1, 2, 0, 2, 0, 7, 2, 1, 5, 1, 12, 12, 12, 12, 5, 7, 9, 4, 20, 10, 9, 6, 17, 20, 18, 7, 6, 11, 9, 24, 3, 22, 8, 24, 33, 35, 33, 31, 12, 0, 27, 6, 31, 37, 37, 27, 31, 6, 24, 7, 17, 12, 1, 39, 41, 51, 48, 21, 8, 15, 26, 46, 52, 43, 39, 7, 21, 60, 24, 58, 21, 57, 58, 36, 60, 25, 7

Offset: 1

Author

Benoit Cloitre, Mar 10 2002

Keywords

• nonn

Examples

			Gamma(3/4) = 1 + 0/2! + 1/3! + 1/4! + 2/5! + 0/6! + 2/7! + ...
		

Links

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

Crossrefs

Cf. A075874, A068465 (decimal expansion), A068464 (Gamma(1/4)).

Programs

Magma

SetDefaultRealField(RealField(250)); [Floor(Gamma(3/4))] cat [Floor(Factorial(n)*Gamma(3/4)) - n*Floor(Factorial((n-1))*Gamma(3/4)) : n in [2..80]]; // G. C. Greubel, Nov 27 2018

Mathematica

With[{b = Gamma[3/4]}, Table[If[n == 1, Floor[b], Floor[n!*b]-n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* G. C. Greubel, Nov 27 2018 *)

PARI

A068463(N=90,c=gamma(precision(.75,logint(N!,10)+1)))=vector(N,n,if(n>1,c=c%1*n,c)\1) \\ - M. F. Hasler, Nov 26 2018

PARI

default(realprecision, 250); b = gamma(3/4); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", ")) \\ G. C. Greubel, Nov 27 2018

Sage

def A068463(n):
    if (n==1): return floor(gamma(3/4))
    else: return expand(floor(factorial(n)*gamma(3/4)) - n*floor(factorial(n-1)*gamma(3/4)))
[A068463(n) for n in (1..80)] # G. C. Greubel, Nov 27 2018

Extensions

Name edited and keywords cons, easy removed by M. F. Hasler, Nov 26 2018