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A248682 Decimal expansion of r = Sum_{n >= 0} (floor(n/2)!)^2/n!. 4
2, 9, 4, 5, 5, 9, 9, 4, 3, 4, 8, 7, 4, 8, 6, 0, 3, 1, 1, 6, 3, 9, 1, 8, 0, 6, 7, 3, 4, 5, 9, 6, 9, 3, 9, 8, 4, 2, 5, 2, 5, 0, 3, 3, 3, 1, 6, 3, 7, 9, 9, 1, 6, 2, 2, 7, 2, 8, 7, 8, 6, 6, 0, 9, 2, 3, 3, 8, 8, 7, 2, 7, 2, 1, 1, 2, 3, 1, 4, 5, 6, 3, 2, 7, 4, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Limit x -> inf., the Sum {n=0..inf} (Floor[n/x])!^x/n! -> e (A001113).

For A248682: x = 2; A248683: x = 3; A248684: x = 4; A248685: x = 5. - Robert G. Wilson v, Feb 22 2016

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

FORMULA

r = Sum_{(n!^2)*p(2,n)/(2*n + 1)!, n >= 0}, where p(k,n) is defined at A248664.

r = Sum_(n >= 0) (floor(n/2)!)^2/n! = Sum_(n >= 1) (3n^2 - 7n + 6)/C(2n, n) = 4/3 + 8*Pi/sqrt(243). - Robert G. Wilson v, Feb 11 2016

EXAMPLE

r = 2.94559943487486031163918067345969398425250...

MATHEMATICA

RealDigits[Sum[(Floor[n/2])!^2/n!, {n, 0, 400}], 10, 111][[1]]

RealDigits[4/3+8Pi/Sqrt[243], 10, 111][[1]]

(* based on Alexander R. Povolotsky, SeqFan Sat 8/18/2012 5PM, Robert G. Wilson v, Feb 10 2016 *)

PROG

(PARI) suminf(n=0, ((n\2)!)^2/n!) \\ Michel Marcus, Feb 11 2016

CROSSREFS

Cf. A248683, A248684, A248785, A248664.

Sequence in context: A019758 A016642 A070700 * A222239 A281384 A203648

Adjacent sequences:  A248679 A248680 A248681 * A248683 A248684 A248685

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Oct 11 2014

STATUS

approved

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Last modified April 20 03:12 EDT 2019. Contains 322294 sequences. (Running on oeis4.)