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.

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A143698 12 times hexagonal numbers: 12*n*(2*n-1).

Original entry on oeis.org

0, 12, 72, 180, 336, 540, 792, 1092, 1440, 1836, 2280, 2772, 3312, 3900, 4536, 5220, 5952, 6732, 7560, 8436, 9360, 10332, 11352, 12420, 13536, 14700, 15912, 17172, 18480, 19836, 21240, 22692, 24192, 25740, 27336, 28980, 30672, 32412
Offset: 0

Views

Author

Omar E. Pol, Jan 23 2009

Keywords

Comments

Sequence found by reading the line from 0, in the direction 0, 12,..., in the square spiral whose vertices are the generalized tetradecagonal numbers A195818. - Omar E. Pol, Oct 02 2011

Links

Crossrefs

Cf. A000384, A002939, A085250, A094159, A152746, A154617.

Programs

Formula

a(n) = 24*n^2 - 12*n = 12*A000384(n) = 6*A002939(n) = 4*A094159(n) = 3*A085250(n) = 2*A152746(n).
a(n) = a(n-1) + 48*n - 36, with a(0)=0. - Vincenzo Librandi, Dec 14 2010
From G. C. Greubel, May 30 2021: (Start)
G.f.: 12*x*(1 + 3*x)/(1-x)^3.
E.g.f.: 12*x*(1 + 2*x)*exp(x). (End)

A273878 Numerator of (2*(n+1)!/(n+2)).

Original entry on oeis.org

1, 4, 3, 48, 40, 1440, 1260, 8960, 72576, 7257600, 6652800, 958003200, 889574400, 11623772160, 163459296000, 41845579776000, 39520825344000, 12804747411456000, 12164510040883200, 231704953159680000, 4644631106519040000
Offset: 0

Views

Author

Johannes W. Meijer, Jun 08 2016

Keywords

Comments

The moments, i.e. E(X^n) = int(x^n * p(x), x = 0..infinity) for n > 0, of the probability density function p(x) = 2*x*E(x, 1, 1), see A163931, lead to this sequence.

Examples

			The first few moments of p(x) are: 1, 4/3, 3, 48/5, 40, 1440/7, … .

Links

Crossrefs

Cf. A090585 (denominators), A090586, A085250, A110468, A128059, A128060, A163931.

Programs

  • Maple
    a := proc(n): numer(2*(n+1)!/(n+2)) end: seq(a(n), n=0..20);
  • PARI
    a(n) = numerator(2*(n+1)!/(n+2)) \\ Felix Fröhlich, Jun 09 2016

Formula

a(n) = numer(2*(n+1)!/(n+2))
a(n) = (n+1) * A090586(n+1)
a(2*n) = A110468(n) and a(2*n+1) = (2*n)!*A085250(n+1)/A128060(n+2).
Previous Showing 21-22 of 22 results.

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

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