cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A051188 Sept-factorial numbers.

Original entry on oeis.org

1, 7, 98, 2058, 57624, 2016840, 84707280, 4150656720, 232436776320, 14643516908160, 1025046183571200, 78928556134982400, 6629998715338521600, 603329883095805465600, 59126328543388935628800
Offset: 0

Views

Author

Wolfdieter Lang

Keywords

Comments

For n >= 1, a(n) is the order of the wreath product of the symmetric group S_n and the Abelian group (C_7)^n. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001

Links

Crossrefs

Cf. A000142, A000165, A032031, A045754, A047053, A047058, A049209, A051186, A052562, A053106, A084947, A092516, A092750, A144827, A144739, A147585.

Programs

Formula

a(n) = n!*7^n =: (7*n)(!^7).
a(n) = 7*A034834(n) = Product_{k=1..n} 7*k, n >= 1.
E.g.f.: 1/(1 - 7*x).
G.f.: 1/(1 - 7*x/(1 - 7*x/(1 - 14*x/(1 - 14*x/(1 - 21*x/(1 - 21*x/(1 - 28*x/(1 - 28*x/(1 - ... (continued fraction). - Philippe Deléham, Jan 08 2012
From Amiram Eldar, Jun 25 2020: (Start)
Sum_{n>=0} 1/a(n) = e^(1/7) (A092516).
Sum_{n>=0} (-1)^n/a(n) = e^(-1/7) (A092750). (End)

A010769 Decimal expansion of 7th root of 2.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Comments

This is also the unique positive attractor of the mapping M(x) = sqrt(sqrt(sqrt(2*x))). In general, (p^N-1)-th root of a number f can be approximated by iterating the mapping M(x) = (f*x)^(1/p^N). The convergence is very fast. In this case, p=2, N=3, and f=2. In the form "evaluate the 3rd (or 7th or 15th) root of a number using only square roots", the insight is usable as a recreational math puzzle. - Stanislav Sykora, Oct 26 2015

Examples

			1.104089513673812337649505387623...

Links

Crossrefs

Cube roots (p=2,N=2) for various f: A002580 (2), A002581 (3), A005480 (4), A010582 (10), A092041 (e). 7th roots (p=2,N=3): A246709 (3), A011186 (4), A011201 (5), A011276 (10), A092516 (e). 8th roots (p=3,N=2): A010770 (2), A246710 (3), A011202 (5), A011277 (10). 15th roots (p=2,N=4): A010777(2), A011194(4), A011209(5), A011284(10). - Stanislav Sykora, Oct 26 2015

Programs

  • Mathematica
    RealDigits[N[2^(1/7), 100]][[1]] (* Vincenzo Librandi, Apr 02 2013 *)
RealDigits[Surd[2,7],10,120][[1]] (* Harvey P. Dale, Sep 05 2022 *)
  • PARI
    sqrtn(2,7) \\ Charles R Greathouse IV, Apr 15 2014
  • PARI
    { default(realprecision, 100); x= 2^(1/7); for(n=1, 100, d=floor(x); x=(x-d)*10; print1(d, ", ")) } \\ Altug Alkan, Nov 14 2015

Formula

Equals Product_{k>=0} (1 + (-1)^k/(7*k + 6)). - Amiram Eldar, Jul 29 2020

A195267 a(n) = 2*n^(2*n)*(1+ sum((1+k^(n+2)/n+k/n)/(n^k*k!), k=1..infinity)) / exp(1/n).

Original entry on oeis.org

14, 89, 3104, 265832, 42711550, 11454711984, 4840928618302, 3108267243405312, 2924919606477510504, 3870562086323220000000, 6908112063470228210507358, 16038451894952529045493383168, 47076979725683125083464370176990, 170928617514191160703263296201650176
Offset: 1

Views

Author

Alexander R. Povolotsky, Sep 14 2011

Keywords

Examples

			n=1: 2*(1+ sum((1+k^3+k)/k!, k=1..infinity))/exp(1) = 14.

Crossrefs

Cf. A001113, A092516, A092514, A092041.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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