A195070 -id:A195070 - cp's OEIS frontend

A196498 Decimal expansion of the constant Sum_{k>=0} (-1)^k/(10*k)!.

9, 9, 9, 9, 9, 9, 7, 2, 4, 4, 2, 6, 8, 0, 7, 7, 6, 0, 5, 5, 2, 1, 2, 5, 2, 3, 6, 7, 5, 8, 0, 2, 0, 4, 7, 6, 0, 0, 1, 2, 6, 3, 7, 2, 0, 3, 6, 6, 0, 0, 3, 5, 6, 2, 1, 1, 9, 7, 3, 3, 1, 6, 3, 7, 2, 8, 9, 9, 3, 3, 6, 5, 8, 4, 7, 2, 1, 1, 6, 8, 9, 6, 7, 4, 0, 0, 2, 7, 4, 8, 2, 1, 1, 9, 7, 3, 8, 4, 2, 5, 9, 3, 0, 1, 0

Offset: 0

R. J. Mathar, Oct 03 2011

			0.99999972442680776055212523675802047...

Michael I. Shamos, A catalog of the real numbers (2011).

Cf. A195070, A195394.

Cf. A068985, A049470, A346441, A346440, A346439, A346438, A346437, A346436, A346435.

RealDigits[ HypergeometricPFQ[{}, {1/10, 1/5, 3/10, 2/5, 1/2, 3/5, 7/10, 4/5, 9/10}, -10^-10], 10, 105] // First (* Jean-François Alcover, Feb 12 2013 *)

sumalt(k=0, (-1)^k/(10*k)!) \\ Michel Marcus, Jul 18 2021

6 more digits from Jean-François Alcover, Feb 12 2013

A195394 a(n) = (10*n)!

Original entry on oeis.org

1, 3628800, 2432902008176640000, 265252859812191058636308480000000, 815915283247897734345611269596115894272000000000, 30414093201713378043612608166064768844377641568960512000000000000

Offset: 0

Vincenzo Librandi, Sep 24 2011

Cf. A000142, A008592, A010050, A100732, A100733, A100734, A195390, A195391, A195392, A195393.

Cf. A195070, A196498.

Magma
```
[Factorial(10*n): n in [0..10]];
```

a[n_] := (10*n)!; Array[a, 6, 0] (* Amiram Eldar, Apr 03 2021 *)
(10*Range[0,10])! (* Harvey P. Dale, Aug 04 2025 *)

From Amiram Eldar, Apr 03 2021: (Start)
a(n) = A000142(A008592(n)).
Sum_{n>=0} 1/a(n) = A195070.
Sum_{n>=0} (-1)^n/a(n) = A196498. (End)

A386440 Decimal expansion of Sum_{k>=1} 1/(8k)!.

Original entry on oeis.org

0, 0, 0, 0, 2, 4, 8, 0, 1, 5, 8, 7, 3, 4, 9, 3, 8, 2, 0, 7, 4, 9, 1, 2, 7, 8, 7, 1, 7, 7, 8, 4, 7, 0, 6, 9, 2, 9, 5, 2, 3, 8, 2, 8, 0, 5, 9, 6, 8, 5, 1, 5, 6, 7, 8, 8, 2, 6, 8, 6, 4, 6, 2, 5, 3, 3, 5, 7, 8, 9, 6, 6, 5, 9, 6, 3, 1, 8, 9, 3, 2, 4, 7, 7, 1, 8, 8, 5, 9, 8, 7, 0, 5, 2, 5, 1, 8, 4, 8, 1, 1, 4, 9, 7

Offset: 0

Jason Bard, Aug 25 2025

			0.00002480158734938207491278717784706929523828059685156788...

Jason Bard, Table of n, a(n) for n = 0..1003
Michael I. Shamos, A catalog of the real numbers, (2007). See p. 21. (Erroneously misses a leading zero)

Cf. A091131, A195070.

RealDigits[-1 + HypergeometricPFQ[{}, Range[1, 7]/8, 2^-24], 10, 100][[1]]

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A196498 Decimal expansion of the constant Sum_{k>=0} (-1)^k/(10*k)!.

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A195394 a(n) = (10*n)!

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A386440 Decimal expansion of Sum_{k>=1} 1/(8k)!.

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