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A096622 Harmonic expansion (or factorial expansion) of the Euler-Mascheroni constant. 3
0, 1, 0, 1, 4, 1, 4, 1, 3, 0, 2, 3, 0, 5, 14, 12, 16, 14, 7, 13, 18, 17, 19, 11, 22, 13, 13, 26, 12, 16, 2, 26, 1, 2, 28, 18, 3, 27, 31, 27, 9, 7, 37, 28, 13, 26, 2, 34, 29, 47, 49, 34, 39, 10, 0, 42, 1, 9, 42, 1, 32, 61, 23, 57, 42, 32, 2, 12, 32, 32, 48, 42, 49, 15, 14, 39, 48 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Harmonic Expansion

Index entries for factorial base representation

FORMULA

Sum_{n>=1} a(n)/n! = Euler gamma = A001620. - G. C. Greubel, Nov 26 2018

EXAMPLE

Euler gamma = 0 + 1/2! + 0/3! + 1/4! + 4/5! + 1/6! + 4/7! + 1/8! + ...

MATHEMATICA

With[{b = EulerGamma}, Table[If[n==1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* G. C. Greubel, Nov 26 2018 *)

PROG

(PARI) default(realprecision, 250); b = Euler; for(n=1, 80, print1( if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", ")) \\ G. C. Greubel, Nov 26 2018

(MAGMA) SetDefaultRealField(RealField(250));  [Floor(EulerGamma(250))] cat [Floor(Factorial(n)*EulerGamma(250)) - n*Floor(Factorial((n-1))*EulerGamma(250)) : n in [2..80]]; // G. C. Greubel, Nov 26 2018

(Sage)

b = euler_gamma;

def A096622(n):

    if (n==1): return floor(b)

    else: return expand(floor(factorial(n)*b) -n*floor(factorial(n-1)*b))

[A096622(n) for n in (1..80)] # G. C. Greubel, Nov 26 2018

CROSSREFS

Cf. A001620 (decimal expansion), A002852 (continued fraction).

Sequence in context: A140704 A030748 A144865 * A331291 A080905 A010685

Adjacent sequences:  A096619 A096620 A096621 * A096623 A096624 A096625

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Jul 01 2004

STATUS

approved

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Last modified April 5 23:04 EDT 2020. Contains 333260 sequences. (Running on oeis4.)