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A068450 Factorial expansion of sqrt(Pi) = Sum_{n>0} a(n)/n!. 3
1, 1, 1, 2, 2, 4, 1, 1, 3, 0, 5, 10, 6, 8, 12, 0, 10, 0, 12, 9, 6, 12, 22, 21, 24, 3, 14, 21, 13, 24, 21, 11, 8, 22, 27, 3, 8, 1, 36, 21, 27, 15, 2, 41, 22, 34, 8, 0, 4, 8, 39, 48, 27, 38, 22, 0, 23, 49, 19, 27, 29, 28, 40, 33, 21, 62, 7, 67, 33, 8, 30, 18, 60, 73, 61, 72, 42, 59, 22 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

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

EXAMPLE

sqrt(Pi) = 1 + 1/2! + 1/3! + 2/4! + 2/5! + 4/6! + 1/7! + ...

MATHEMATICA

Table[If[n == 1, Floor[Sqrt[Pi]], Floor[n!*Sqrt[Pi]] - n*Floor[(n - 1)!*Sqrt[Pi]]], {n, 1, 50}] (* G. C. Greubel, Mar 21 2018 *)

PROG

(PARI) default(realprecision, 250); for(n=1, 30, print1(if(n==1, floor(sqrt(Pi)), floor(n!*sqrt(Pi)) - n*floor((n-1)!*sqrt(Pi))), ", ")) \\ G. C. Greubel, Mar 21 2018

(PARI) vector(30, n, if(n>1, t=t%1*n, t=sqrt(Pi))\1) \\ M. F. Hasler, Nov 25 2018

(MAGMA) SetDefaultRealField(RealField(250));  R:= RealField(); [Floor(Sqrt(Pi(R)))] cat [Floor(Factorial(n)*Sqrt(Pi(R))) - n*Floor(Factorial((n-1))*Sqrt(Pi(R))) : n in [2..30]]; // G. C. Greubel, Mar 21 2018

(Sage)

def A068450(n):

    if (n==1): return floor(sqrt(pi))

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

[A068450(n) for n in (1..80)] # G. C. Greubel, Nov 27 2018

CROSSREFS

Cf. A075874, A002161 (decimal expansion).

Sequence in context: A282627 A004565 A068449 * A071436 A214741 A243487

Adjacent sequences:  A068447 A068448 A068449 * A068451 A068452 A068453

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Mar 10 2002

EXTENSIONS

Keyword cons removed by R. J. Mathar, Jul 23 2009

STATUS

approved

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Last modified June 26 13:53 EDT 2022. Contains 354883 sequences. (Running on oeis4.)