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 1-7 of 7 results.

A128960 a(n) = (n^3 - n)*2^n.

Original entry on oeis.org

0, 24, 192, 960, 3840, 13440, 43008, 129024, 368640, 1013760, 2703360, 7028736, 17891328, 44728320, 110100480, 267386880, 641728512, 1524105216, 3586129920, 8367636480, 19377684480, 44568674304, 101871255552, 231525580800, 523449139200, 1177760563200, 2638183661568
Offset: 1

Views

Author

Mohammad K. Azarian, Apr 28 2007

Keywords

Links

Crossrefs

Cf. A000079, A007531, A036289, A128796.
Cf. A128961, A128962, A128963, A128964, A128965, A128967, A128969.

Programs

  • Magma
    [(n^3-n)*2^n: n in [1..25]]; /* or */ I:=[0,24,192,960]; [n le 4 select I[n] else 8*Self(n-1)-24*Self(n-2)+32*Self(n-3)-16*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Feb 12 2013
  • Mathematica
    CoefficientList[Series[24 x/(1 - 2 x)^4, {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -24, 32, -16}, {0, 24, 192, 960}, 30] (* Vincenzo Librandi, Feb 12 2013 *)
  • PARI
    a(n)=(n^3-n)<Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: 24*x^2/(1-2*x)^4. - Vincenzo Librandi, Feb 12 2013
a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4). - Vincenzo Librandi, Feb 12 2013
From Amiram Eldar, Oct 02 2022: (Start)
a(n) = A007531(n+1)*A000079(n).
Sum_{n>=2} 1/a(n) = (2*log(2)-1)/8.
Sum_{n>=2} (-1)^n/a(n) = (3/2)^2*log(3/2) - 7/8. (End)

Extensions

Offset corrected by Mohammad K. Azarian, Nov 19 2008

A128964 a(n) = (n^3-n)*6^n.

Original entry on oeis.org

0, 216, 5184, 77760, 933120, 9797760, 94058496, 846526464, 7255941120, 59861514240, 478892113920, 3735358488576, 28524555730944, 213934167982080, 1579821548175360, 11510128422420480, 82872924641427456, 590469588070170624, 4168020621671792640, 29176144351702548480
Offset: 1

Views

Author

Mohammad K. Azarian, Apr 28 2007

Keywords

Links

Crossrefs

Cf. A000400, A007531, A036289, A081144, A128796.
Cf. A128960, A128961, A128962, A128963, A128965, A128967, A128969.

Programs

  • Magma
    [(n^3-n)*6^n: n in [1..25]]; // Vincenzo Librandi, Feb 11 2013
  • Magma
    I:=[0, 216, 5184, 77760]; [n le 4 select I[n] else 24*Self(n-1) -216*Self(n-2) +864*Self(n-3) -1296*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Feb 11 2013
  • Mathematica
    CoefficientList[Series[216 x/(1 - 6 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 11 2013 *)

Formula

From R. J. Mathar, Dec 19 2008: (Start)
G.f.: 216*x^2/(1-6*x)^4.
a(n) = 216*A081144(n+1). (End)
a(n) = 24*a(n-1) - 216*a(n-2) + 864*a(n-3) - 1296*a(n-4). - Vincenzo Librandi, Feb 11 2013
From Amiram Eldar, Jan 04 2022: (Start)
Sum_{n>=2} 1/a(n) = 25*log(6/5)/12 - 3/8.
Sum_{n>=2} (-1)^n/a(n) = 49*log(7/6)/12 - 5/8. (End)
a(n) = A007531(n+1)*A000400(n). - Amiram Eldar, Oct 02 2022

Extensions

Corrected offset. - Mohammad K. Azarian, Nov 20 2008

A128961 a(n) = (n^3 - n)*3^n.

Original entry on oeis.org

0, 54, 648, 4860, 29160, 153090, 734832, 3306744, 14171760, 58458510, 233834040, 911952756, 3482001432, 13057505370, 48212327520, 175630621680, 632270238048, 2252462723046, 7949868434280, 27824539519980, 96653663595720, 333455139405234, 1143274763675088
Offset: 1

Views

Author

Mohammad K. Azarian, Apr 28 2007

Keywords

Links

Crossrefs

Cf. A000244, A007531, A036289, A128796.
Cf. A128960, A128962, A128963, A128964, A128965, A128967, A128969.

Programs

  • Magma
    [(n^3-n)*3^n: n in [1..25]]; // Vincenzo Librandi, Feb 12 2013
  • Magma
    I:=[0,54,648,4860]; [n le 4 select I[n] else 12*Self(n-1)-54*Self(n-2)+108*Self(n-3)-81*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Feb 12 2013
  • Mathematica
    LinearRecurrence[{12, -54, 108, -81}, {0, 54, 648, 4860}, 30] (* or *) CoefficientList[Series[54 x/(1 - 3 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 12 2013 *)

Formula

G.f.: 54*x^2/(1-3*x)^4. - Vincenzo Librandi, Feb 12 2013
a(n) = 12*a(n-1) - 54*a(n-2) + 108*a(n-3) - 81*a(n-4). - Vincenzo Librandi, Feb 12 2013
From Amiram Eldar, Oct 02 2022: (Start)
a(n) = A007531(n+1)*A000244(n).
Sum_{n>=2} 1/a(n) = (2/3)*log(3/2) - 1/4.
Sum_{n>=2} (-1)^n/a(n) = (8/3)*log(4/3) - 3/4. (End)

Extensions

Offset corrected by Mohammad K. Azarian, Nov 20 2008

A128962 a(n) = (n^3 - n)*4^n.

Original entry on oeis.org

0, 96, 1536, 15360, 122880, 860160, 5505024, 33030144, 188743680, 1038090240, 5536481280, 28789702656, 146565758976, 732828794880, 3607772528640, 17523466567680, 84112639524864, 399535037743104, 1880164883496960, 8774102789652480, 40637949762600960
Offset: 1

Views

Author

Mohammad K. Azarian, Apr 28 2007

Keywords

Links

Crossrefs

Cf. A000302, A007531, A036289, A128796.
Cf. A128960, A128961, A128963, A128964, A128965, A128967, A128969.

Programs

  • Magma
    [(n^3-n)*4^n: n in [1..20]]; // Vincenzo Librandi, Feb 09 2013
  • Mathematica
    CoefficientList[Series[96 x / (1-4 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 09 2013 *)
Table[(n^3-n)4^n,{n,20}] (* or *) LinearRecurrence[{16,-96,256,-256},{0,96,1536,15360},20] (* Harvey P. Dale, Dec 31 2018 *)

Formula

G.f.: 96*x^2/(1-4*x)^4. - Vincenzo Librandi, Feb 09 2013
a(n) = 16*a(n-1) - 96*a(n-2) + 256*a(n-3) - 256*a(n-4). - Vincenzo Librandi, Feb 09 2013
a(n) = 96*A038846(n-2) for n>1. - Bruno Berselli, Feb 10 2013
From Amiram Eldar, Oct 02 2022: (Start)
a(n) = A007531(n+1)*A000302(n).
Sum_{n>=2} 1/a(n) = (9/8)*log(4/3) - 5/16.
Sum_{n>=2} (-1)^n/a(n) = (25/8)*log(5/4) - 11/16. (End)

Extensions

Offset corrected by Mohammad K. Azarian, Nov 20 2008

A128963 a(n) = (n^3 - n)*5^n.

Original entry on oeis.org

0, 150, 3000, 37500, 375000, 3281250, 26250000, 196875000, 1406250000, 9667968750, 64453125000, 418945312500, 2666015625000, 16662597656250, 102539062500000, 622558593750000, 3735351562500000, 22178649902343750, 130462646484375000, 761032104492187500
Offset: 1

Views

Author

Mohammad K. Azarian, Apr 28 2007

Keywords

Links

Crossrefs

Cf. A000351, A007531, A036289, A081143, A128796.
Cf. A128960, A128961, A128962, A128964, A128965, A128967, A128969.

Programs

  • Magma
    [(n^3-n)*5^n: n in [1..25]]; // Vincenzo Librandi, Feb 12 2013
  • Mathematica
    Table[(n^3-n)5^n,{n,20}] (* or *) LinearRecurrence[{20,-150,500,-625},{0,150,3000,37500},20] (* Harvey P. Dale, Jul 22 2012 *)
CoefficientList[Series[150 x/(1 - 5 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 12 2013 *)

Formula

a(1)=0, a(2)=150, a(3)=3000, a(4)=37500, a(n)=20*a(n-1)-150*a(n-2)+ 500*a(n-3)- 625*a(n-4). - Harvey P. Dale, Jul 22 2012
G.f.: 150*x^2/(1 - 5*x)^4. - Vincenzo Librandi, Feb 12 2013
a(n) = 150*A081143(n+1). - Bruno Berselli, Feb 12 2013
From Amiram Eldar, Oct 02 2022: (Start)
a(n) = A007531(n+1)*A000351(n).
Sum_{n>=2} 1/a(n) = (8/5)*log(5/4) - 7/20.
Sum_{n>=2} (-1)^n/a(n) = (18/5)*log(6/5) - 13/20. (End)

Extensions

Offset corrected by Mohammad K. Azarian, Nov 20 2008

A128965 a(n) = (n^3 - n)*7^n.

Original entry on oeis.org

0, 294, 8232, 144060, 2016840, 24706290, 276710448, 2905459704, 29054597040, 279650496510, 2610071300760, 23751648836916, 211605598728888, 1851548988877770, 15951806673408480, 135590356723972080, 1138958996481365472, 9467596658251350486, 77968443067952298120
Offset: 1

Views

Author

Mohammad K. Azarian, Apr 28 2007

Keywords

Links

Crossrefs

Cf. A000420, A007531, A036289, A128796, A140107.
Cf. A128960, A128961, A128962, A128963, A128964, A128967, A128969.

Programs

  • Magma
    [(n^3 - n)*7^n: n in [1..25]]; // Vincenzo Librandi, Feb 11 2013
  • Mathematica
    LinearRecurrence[{28, -294, 1372, -2401}, {0, 294, 8232, 144060}, 30] (* Vincenzo Librandi, Feb 11 2013 *)
Table[(n^3-n)7^n,{n,20}] (* Harvey P. Dale, May 14 2020 *)

Formula

From R. J. Mathar, Dec 19 2008: (Start)
G.f.: 294x^2/(1-7x)^4.
a(n) = 294*A140107(n-2). (End)
a(n) = 28*a(n-1) - 294*a(n-2) + 1372*a(n-3) - 2401*a(n-4). - Vincenzo Librandi, Feb 11 2013
From Amiram Eldar, Oct 02 2022: (Start)
a(n) = A007531(n+1)*A000420(n).
Sum_{n>=2} 1/a(n) = (18/7)*log(7/6) - 11/28.
Sum_{n>=2} (-1)^n/a(n) = (32/7)*log(8/7) - 17/28. (End)

Extensions

Offset corrected by Mohammad K. Azarian, Nov 20 2008

A128969 a(n) = (n^3 - n)*9^n.

Original entry on oeis.org

0, 486, 17496, 393660, 7085880, 111602610, 1607077584, 21695547384, 278942752080, 3451916556990, 41422998683880, 484649084601396, 5551434969070536, 62453643402043530, 691794203838020640, 7560322370515511280, 81651481601567521824, 872650209616752889494
Offset: 1

Views

Author

Mohammad K. Azarian, Apr 28 2007

Keywords

Links

Crossrefs

Cf. A001019, A007531, A036289, A038291, A128796.
Cf. A128960, A128961, A128962, A128963, A128964, A128965, A128967.

Programs

  • Magma
    [(n^3-n)*9^n: n in [0..25]]; // Vincenzo Librandi, Feb 11 2013
  • Magma
    I:=[0, 486, 17496, 393660]; [n le 4 select I[n] else 36*Self(n-1) - 486*Self(n-2) + 2916*Self(n-3) - 6561*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Feb 11 2013
  • Mathematica
    CoefficientList[Series[486 x/(1 - 9 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 11 2013 *)

Formula

From R. J. Mathar, Dec 19 2008 (Start)
G.f.: 486x^2/(1-9x)^4.
a(n) = 486*A038291(n+1,3). (End)
a(n) = 36*a(n-1) - 486*a(n-2) + 2916*a(n-3) - 6561*a(n-4). - Vincenzo Librandi, Feb 11 2013
From Amiram Eldar, Oct 02 2022: (Start)
a(n) = A007531(n+1)*A001019(n).
Sum_{n>=2} 1/a(n) = (32/9)*log(9/8) - 5/12.
Sum_{n>=2} (-1)^n/a(n) = (50/9)*log(10/9) - 7/12. (End)

Extensions

Offset corrected by Mohammad K. Azarian, Nov 20 2008
Showing 1-7 of 7 results.

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

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