A322509 Factorial expansion of Gamma(2/3) = Sum_{n>=1} a(n)/n!.

1, 0, 2, 0, 2, 2, 6, 6, 0, 3, 1, 11, 7, 6, 6, 14, 1, 8, 12, 15, 8, 17, 8, 1, 13, 15, 3, 4, 10, 16, 25, 1, 25, 22, 6, 3, 19, 17, 8, 10, 25, 37, 29, 17, 35, 19, 24, 25, 30, 31, 4, 7, 51, 49, 14, 51, 45, 54, 0, 26, 34, 41, 56, 57, 16, 15, 63, 4, 51, 42, 13, 35, 12, 15, 66, 22, 13, 43, 14, 78

Offset

1,3

Links

Table of n, a(n) for n=1..80.

Index entries for factorial base representation

Example

Gamma(2/3) = 1 + 0/2! + 2/3! + 0/4! + 2/5! + 2/6! + 6/7! + 6/8! + ...

Mathematica

With[{b = Gamma[2/3]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]]

Prog

(PARI) default(realprecision, 250); b = gamma(2/3); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", "))
(Magma) SetDefaultRealField(RealField(250));  [Floor(Gamma(2/3))] cat [Floor(Factorial(n)*Gamma(2/3)) - n*Floor(Factorial((n-1))*Gamma(2/3)) : n in [2..80]];
(Sage)
b=gamma(2/3);
def a(n):
    if (n==1): return floor(b)
    else: return expand(floor(factorial(n)*b) -n*floor(factorial(n-1)*b))
[a(n) for n in (1..80)]

Crossrefs

Cf. A073006 (decimal expansion), A030652 (continued fraction).

Cf. A068463 (Gamma(3/4)), A068464 (Gamma(1/4)), A322508 (Gamma(1/3)).

Sequence in context: A354101 A078052 A056458 * A284570 A256847 A372023

Adjacent sequences: A322506 A322507 A322508 * A322510 A322511 A322512

Keyword

nonn

Author

G. C. Greubel, Dec 12 2018

Status

approved