A165457 -id:A165457 - cp's OEIS frontend

A135003 Decimal expansion of 3/e.

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

Offset: 1

Omar E. Pol, Nov 15 2007

			1.103638323514...

G. C. Greubel, Table of n, a(n) for n = 1..2000

Cf. A001113, A068985, A165457.

RealDigits[3/E , 10, 50][[1]] (* G. C. Greubel, Sep 16 2016 *)

PARI
```
3/exp(1) \\ Michel Marcus, Sep 16 2016
```

Equals Sum_{n>=0} 1/A165457(n). - Jaume Oliver Lafont, Oct 03 2009
Equals 3/A001113 and 3*A068985. - Michel Marcus, Sep 16 2016
Equals 1 - Integral_{x=-1/e..0} W(x) dx, where W is Lambert's function. - Amiram Eldar, Jul 18 2021

Minor edits by Omar E. Pol, Oct 07 2009

A174549 a(n) = (2n-1)! + (2n)!.

Original entry on oeis.org

3, 30, 840, 45360, 3991680, 518918400, 93405312000, 22230464256000, 6758061133824000, 2554547108585472000, 1175091669949317120000, 646300418472124416000000, 418802671169936621568000000, 315777214062132212662272000000, 274094621805930760590852096000000

Offset: 1

Paul Curtz, Mar 22 2010

x*cos(x) - sin(x) = Sum_{n>=1} (-1)^n/a(n) * x^(2*n+1). - James R. Buddenhagen, Nov 21 2013

Also the number of adjacency matrices for the n-helm graph. - Eric W. Weisstein, May 25 2017

Vincenzo Librandi, Table of n, a(n) for n = 1..100
Eric Weisstein's World of Mathematics, Adjacency Matrix.
Eric Weisstein's World of Mathematics, Helm Graph.

Cf. A001048, A000255, A068985, A143624, A165457.

[Factorial(2*n-1) + Factorial(2*n): n in [1..15]]; // Vincenzo Librandi, Aug 04 2011

A174549 := proc(n) (1+2*n)*(2*n-1)! ; end proc: # R. J. Mathar, Jan 13 2011

Table[(2*n - 1)! + (2*n)!, {n, 15}] (* T. D. Noe, Nov 21 2013 *)

a(n)=(2*n-1)!*(2*n+1) \\ Charles R Greathouse IV, Nov 21 2013

a(n) = A001048(2n) = (1+2n)*(2n-1)! = 3*A165457(n-1).
Sum_{n>=1} 1/a(n) = A068985 = 1/e = lim_{n->infinity} A000255(n-1)/A001048(n).
zeta(2*n+1) = Integral_{u=0..Pi/2} (sin(u)*log(sin(u))^(2*n+1)/(cos(u)^3))*(-2)^(2*n+1)/(n*a(n)) du. Verified for n=1 to 4 on Wolfram Alpha. - Jean-Claude Babois, Oct 28 2014
Sum_{n>=1} (-1)^(n+1)/a(n) = sin(1)-cos(1) = (-1)*A143624. - Amiram Eldar, Apr 12 2021

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A135003 Decimal expansion of 3/e.

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A174549 a(n) = (2n-1)! + (2n)!.

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cp's OEIS Frontend

A135003 Decimal expansion of 3/e.

Views

Author

Keywords

Examples

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Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A174549 a(n) = (2*n-1)! + (2*n)!.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

A174549 a(n) = (2n-1)! + (2n)!.