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 1-4 of 4 results.

A058077 Binomial coefficients formed from consecutive primes: a(n) = binomial( prime(n+1), prime(n) ).

Original entry on oeis.org

3, 10, 21, 330, 78, 2380, 171, 8855, 475020, 465, 2324784, 101270, 903, 178365, 22957480, 45057474, 1830, 99795696, 971635, 2628, 277962685, 1837620, 581106988, 144520208820, 4082925, 5253, 5160610, 5886, 6438740
Offset: 1

Views

Author

Labos Elemer, Nov 13 2000

Keywords

Comments

Conjecture: for each value of n > 1, if a(n+1) has the same number of digits as a(n) and a(n+1) > a(n), then prime(n+2) - prime(n+1) = prime(n+1) - prime(n). This conjecture has been verified for all n < 3*10^7. - Ahmad J. Masad, Oct 08 2019

Examples

			n=6: a(6) = C(p(7),p(6)) = C(17,13) = 57120/24 = 2380.

Links

Crossrefs

Cf. A000040, A001223.
Cf. A037293, A066526, A080911, A277341.

Programs

  • Mathematica
    Table[Binomial[Prime[n+1],Prime[n]],{n,1,20}] (* Vaclav Kotesovec, Nov 13 2014 *)

Formula

a(n) = binomial(A000040(n+1), A001223(n)).

Extensions

Offset corrected by Vaclav Kotesovec, Nov 13 2014

A060001 a(n) = Fibonacci(n)!.

Original entry on oeis.org

1, 1, 2, 6, 120, 40320, 6227020800, 51090942171709440000, 295232799039604140847618609643520000000, 12696403353658275925965100847566516959580321051449436762275840000000000000
Offset: 1

Views

Author

Jason Earls, Mar 14 2001

Keywords

Links

Crossrefs

Cf. A000045, A000142, A003266, A066526, A327558.

Programs

Formula

From Amiram Eldar, Nov 20 2020: (Start)
a(n) = A000142(A000045(n)).
Sum_{n>=1} 1/a(n) = A327558. (End)

A080911 a(n) = binomial(n!,(n-1)!).

Original entry on oeis.org

1, 2, 15, 134596, 10872202353646160680764975
Offset: 1

Views

Author

Labos Elemer, Apr 01 2003

Keywords

Links

Crossrefs

Cf. A000142, A037293, A066526, A058077.

Programs

  • Mathematica
    Table[Binomial[n!, (n-1)!], {n, 1, 7}] (* Vaclav Kotesovec, Nov 13 2014 *)

A334575 a(n) = binomial(C(n+1),C(n)) where C(n) = A000108(n) the n-th Catalan number.

Original entry on oeis.org

1, 2, 10, 2002, 52860229080, 53570336911983273963270306331114400
Offset: 0

Views

Author

Henry Cryns, May 06 2020

Keywords

Crossrefs

Cf. A000108, A058077, A066526, A080911.
Showing 1-4 of 4 results.

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

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