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.

A233446 a(n) = ((2n-1)^(2n+1) + (2n+1)^(2n-1))/(2n)^2 = A154682(n)/(2n)^2 for n > 0.

Original entry on oeis.org

1, 23, 2637, 705259, 337390073, 252186614847, 271082082053317, 396049017137512403, 754792662169555947633, 1818644980834260579498343, 5405067064522549127719680701, 19423396040054801221090342470843, 83016890560608261435356904433668457, 416213066932582983199004231480676255119, 2419095491735191624607023665166934072373813
Offset: 1

Views

Author

Alexander Adamchuk, Dec 10 2013

Keywords

Crossrefs

Cf. A154682.

Programs

  • Mathematica
    Table[((2 n - 1)^(2 n + 1) + (2 n + 1)^(2 n - 1))/(2 n)^2, {n, 1, 15}]

Formula

a(n) = ((2n-1)^(2n+1) + (2n+1)^(2n-1))/(2n)^2; n > 0.

A154569 Partial sums of (2n-1)^(2n+1)+(2n+1)^(2n-1).

Original entry on oeis.org

0, 4, 372, 95304, 45231880, 33784239180, 36348656777148, 53168436739227280, 101441716823942402448, 244654264259760069435540, 727702646597963991868772740, 2616780161875511741808194232024, 11190492899233441015089845457437592
Offset: 0

Views

Author

Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 12 2009

Keywords

Comments

All the terms of the sequence are divisible by 4, a(0) = 0 by default.

Crossrefs

Cf. A154682.

Programs

  • Mathematica
    Accumulate[Table[(2n-1)^(2n+1)+(2n+1)^(2n-1),{n,20}]] (* Harvey P. Dale, Jun 05 2012 *)

Formula

a(n) = a(n-1)+(2n-1)^(2n+1)+(2n+1)^(2n-1).
a(n) = sum_{k=0..n} A051489(2k-1). - R. J. Mathar, Jan 14 2009

Extensions

More terms from Harvey P. Dale, Jun 05 2012

A234252 a(n) = ((n-1)^(n+1) + (-1)^n*(n+1)^(n-1))/(n^2).

Original entry on oeis.org

-1, 1, 0, 23, 112, 2637, 28928, 705259, 12021504, 337390073, 7752749056, 252186614847, 7261683740672, 271082082053317, 9359536638984192, 396049017137512403, 15920162462882529280, 754792662169555947633, 34587513064809080815616, 1818644980834260579498343
Offset: 1

Views

Author

Alexander Adamchuk, Dec 22 2013

Keywords

Comments

a(2n) = A233446(n) = ((2n-1)^(2n+1) + (2n+1)^(2n-1))/(2n)^2 = A154682(n)/(2n)^2 for n > 0.

Crossrefs

Cf. A154682, A233446.

Programs

  • Mathematica
    Table[((m-1)^(m+1)+(-1)^m*(m+1)^(m-1))/(m^2),{m,1,20}]
  • PARI
    a(n) = ((n-1)^(n+1) + (-1)^n*(n+1)^(n-1))/n^2; \\ Michel Marcus, Jun 06 2021

Formula

a(n) = ((n-1)^(n+1) + (-1)^n*(n+1)^(n-1))/(n^2).
Showing 1-3 of 3 results.

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

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