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 1-8 of 8 results.

A173797 Partial sums of A046065.

Original entry on oeis.org

-1, -3, -3, 115, 2915, 64233, 1481705, 37052343, 1010794167, 30033906085, 968116541861, 33698668291755, 1260923220465323, 50500621166196705, 2156396364937639905, 97820098649121183487, 4698747050422172145407
Offset: 0

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 24 2010

Keywords

Links

Crossrefs

Cf. A046065.

Programs

  • Magma
    [(&+[j^(j+2) - (j+2)^j: j in [0..n]]): n in [0..40]]; // G. C. Greubel, Jul 14 2021
  • Mathematica
    f[n_]:=(n^(n+2)-(n+2)^n); s=0; Table[s+=f[n],{n,0,40}]
  • Sage
    [sum(j^(j+2) - (j+2)^j for j in (0..n)) for n in (0..40)] # G. C. Greubel, Jul 14 2021

Formula

a(n) = Sum_{j=0..n} A046065(j). - G. C. Greubel, Jul 14 2021

A055651 Table T(m,k)=m^k-k^m (with 0^0 taken to be 1) as square array read by antidiagonals.

Original entry on oeis.org

0, 1, -1, 1, 0, -1, 1, 1, -1, -1, 1, 2, 0, -2, -1, 1, 3, 1, -1, -3, -1, 1, 4, 0, 0, 0, -4, -1, 1, 5, -7, -17, 17, 7, -5, -1, 1, 6, -28, -118, 0, 118, 28, -6, -1, 1, 7, -79, -513, -399, 399, 513, 79, -7, -1, 1, 8, -192, -1844, -2800, 0, 2800, 1844, 192, -8, -1, 1, 9, -431
Offset: 0

Views

Author

Henry Bottomley, Jun 07 2000

Keywords

Crossrefs

Rows A000012 (offset), A023443, A024012, A024026, A024040 and diagonals A000004, A007925, A046065, A055652.

Extensions

Title corrected by Sean A. Irvine, Mar 30 2022

A051489 a(n) = n^(n+2) + (n+2)^n.

Original entry on oeis.org

1, 4, 32, 368, 5392, 94932, 1941760, 45136576, 1173741824, 33739007300, 1061917364224, 36314872537968, 1340612376924160, 53132088082450132, 2250010931847299072, 101388548387203175168, 4843806013966239465472
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A007925, A046065, A051442. - Vladimir Joseph Stephan Orlovsky, Jan 23 2009

Programs

  • Magma
    [n^(n+2) + (n+2)^n: n in [0..30]]; // G. C. Greubel, Jul 14 2021
  • Mathematica
    Table[n^(n+2)+(n+2)^n,{n,0,20}] (* Harvey P. Dale, Jul 28 2025 *)
  • Sage
    [n^(n+2) + (n+2)^n for n in (0..30)] # G. C. Greubel, Jul 14 2021

A101334 a(n) = n^n - (n+1)^(n-1).

Original entry on oeis.org

0, 0, 1, 11, 131, 1829, 29849, 561399, 11994247, 287420489, 7642052309, 223394306387, 7123940054219, 246181194216957, 9165811757198641, 365836296342931439, 15584321022199735823, 705800730789742512401, 33866021217511735389485, 1716275655660313589123979
Offset: 0

Views

Author

Jorge Coveiro, Dec 24 2004

Keywords

Comments

b(n) = n^n mod (n+1)^(n-1) begins: 0, 0, 1, 11, 6, 533, 13042, 37111, 2428309, ... - Alex Ratushnyak, Aug 06 2012
a(n) is the number of functions f:{1,2,...,n}->{1,2,...,n} with at least one cycle of length >= 2. - Geoffrey Critzer, Jan 11 2013
Number of defective parking functions of length n and at least one defect. - Alois P. Heinz, Aug 18 2017

Examples

			a(3) = 3^3 - 4^2 = 27-16 = 11.

Links

Crossrefs

Cf. A000272, A000312, A046065, A264902.

Programs

  • Mathematica
    ReplacePart[Table[n^n-(n+1)^(n-1),{n,0,nn}],0,1]  (* Geoffrey Critzer, Jan 11 2013 *)
  • PARI
    for(x=1,20,print( x^x-(x+1)^(x-1) ))
  • Python
    print([n**n - (n+1)**(n-1) for n in range(33)]) # Alex Ratushnyak, Aug 06 2012

Formula

E.g.f.: 1/(1-T(x)) - exp(T(x)) where T(x) is the e.g.f. for A000169. - Geoffrey Critzer, Jan 11 2013
a(n) = Sum_{k>0} A264902(n,k). - Alois P. Heinz, Nov 29 2015
a(n) = A000312(n) - A000272(n+1). - Alois P. Heinz, Aug 18 2017

Extensions

a(0) prepended by Alex Ratushnyak, Aug 06 2012

A155539 a(n) = n^(n+3) + (n+3)^n.

Original entry on oeis.org

1, 5, 57, 945, 18785, 423393, 10609137, 292475249, 8804293473, 287589316833, 10137858491849, 383799398752905, 15536767912476993, 669920208810550337, 30659724555890596833, 1484638520651877849057, 75846305139481944586817
Offset: 0

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 23 2009

Keywords

Comments

1^4 + 4^1 = 5, 2^5 + 5^2 = 57, ...

Links

Crossrefs

Cf. A046065, A051442, A007925, A051489, A153217, A076980.

Programs

  • Magma
    [n^(n+3)+(n+3)^n: n in [0..20] ]; // Vincenzo Librandi, Aug 25 2011
  • Mathematica
    lst={};Do[m=n+3;q=n^m+m^n;AppendTo[lst,q],{n,0,4!}];lst
Table[n^(n+3)+(n+3)^n,{n,0,20}] (* Harvey P. Dale, Aug 18 2024 *)

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 24 2011

A215265 a(n) = (n-1)^(n+1) - n^n.

Original entry on oeis.org

-2, -1, -3, -11, -13, 971, 31469, 856073, 23576391, 686321335, 21381059609, 714688329389, 25606611695675, 981043357956611, 40073886188532741, 1740059447428511761, 80079381261983807759, 3895126220983308449519, 199726027609854787271729, 10769816560735764585313397
Offset: 0

Views

Author

Alex Ratushnyak, Aug 07 2012

Keywords

Comments

0^0 is interpreted as 1.

Examples

			a(3) = 2^4 - 3^3 = 16-27 = -11.

Links

Crossrefs

Cf. A101334, A046065.
Cf. A064232 is essentially equal to (n-1)^(n+1) mod n^n.

Programs

  • Maple
    A215265 := proc(n)
    (n-1)^(n+1)-n^n ;
end proc: # R. J. Mathar, Aug 07 2012
  • Mathematica
    Join[{-2},Table[(n-1)^(n+1)-n^n,{n,20}]] (* Harvey P. Dale, May 21 2023 *)
  • Python
    for n in range(33):
    print((n-1)**(n+1) - n**n)

Formula

For n>0, a(n) = A046065(n-1) - A101334(n).
E.g.f.: x/W(-x) - (1+x)/(1+W(-x)) - x/(1+W(-x))^2 + x/(1+W(-x))^3, where W is the Lambert W function. - Robert Israel, Mar 29 2017

A153217 a(n)=n^(n+3)-(n+3)^n.

Original entry on oeis.org

-1, -3, 7, 513, 13983, 357857, 9546255, 272475249, 8375575711, 277269756129, 9862141508151, 375700268413577, 15277275236695743, 660913009555809345, 30322968902771794975, 1471145239418922932193, 75269422312346702251455
Offset: 0

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 20 2008

Keywords

Crossrefs

Cf. A046065

Programs

  • Mathematica
    a[n_]:=n^(n+3)-(n+3)^n;lst={};Do[AppendTo[lst,a[n]],{n,0,4!}];lst
Table[n^(n+3)-(n+3)^n,{n,0,20}] (* Harvey P. Dale, Jan 27 2014 *)

Extensions

Minor edits from Harry J. Smith, Dec 23 2008

A094647 a(n) = n^(2n) - (2n)^n.

Original entry on oeis.org

-1, 0, 513, 61440, 9665625, 2173796352, 678117659345, 281470681743360, 150094436937708753, 99999989760000000000, 81402748802521459701993, 79496847166870496697384960, 91733330190787463785195879433
Offset: 1

Views

Author

Gregory S. Thoman (fealuinix(AT)yahoo.com), May 18 2004

Keywords

Examples

			a(3) = 513 because 3^(2*3) - (2*3)^3 = 3^6 - 6^3 = 513.

Crossrefs

Cf. A007925, A046065.

Programs

  • Mathematica
    a[n_] := n^n(n^n - 2^n); Table[a[n], {n, 13}] (* Robert G. Wilson v, May 24 2004 *)

Extensions

More terms from Emeric Deutsch, Robert G. Wilson v and Pab Ter (pabrlos(AT)yahoo.com), May 24 2004
Showing 1-8 of 8 results.

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