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.

Previous Showing 21-30 of 40 results. Next

A145616 Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=4.

Original entry on oeis.org

1, 3, 5, 70, 315, 3465, 45045, 36036, 51051, 4849845, 1616615, 223092870, 557732175, 5019589575, 145568097675, 36100888223400, 410237366175, 410237366175, 15178782548475, 30357565096950, 622330084487475
Offset: 1

Views

Author

Artur Jasinski, Oct 14 2008

Keywords

Comments

For numerators see A145615. For general properties of A_l(x) see A145609.

Crossrefs

Cf. A145609 - A145640.

Programs

  • Mathematica
    m = 4; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Denominator[k]], {r, 1, 30}]; aa (*Artur Jasinski*)

Extensions

Edited by R. J. Mathar, Aug 21 2009

A145617 Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=5.

Original entry on oeis.org

55, 8365, 209195, 73218955, 5491423277, 1510141416085, 490795960391965, 24539798019883535, 10429414158454786655, 4953971725266096561953, 11259026648332043641555, 6473940322790925219990095
Offset: 1

Views

Author

Artur Jasinski, Oct 14 2008

Keywords

Comments

For denominators see A145618. For general properties of A_l(x) see A145609.

Crossrefs

Cf. A145609 - A145640.

Programs

  • Mathematica
    m = 5; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Numerator[k]], {r, 1, 25}]; aa (* Artur Jasinski *)
a[n_,m_]:=Integrate[(m-x^n)/(m-x),{x,0,1}]+(m^n-m)Log[m/(m-1)]
Table[5 a[2 n, 5] // FullSimplify  // Numerator, {n,1,25}]  (* Gerry Martens , Jun 04 2016 *)

Extensions

Edited by R. J. Mathar, Aug 21 2009

A145618 Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=5.

Original entry on oeis.org

2, 12, 12, 168, 504, 5544, 72072, 144144, 2450448, 46558512, 4232592, 97349616, 97349616, 41721264, 1209916656, 75014832672, 825163159392, 5776142115744, 213717258282528, 213717258282528, 1251772512797664, 53826218050299552
Offset: 1

Views

Author

Artur Jasinski, Oct 14 2008

Keywords

Comments

For numerators see A145617. For general properties of A_l(x) see A145609.

Crossrefs

Cf. A145609 - A145640.

Extensions

Edited by R. J. Mathar, Aug 21 2009

A145619 Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=6.

Original entry on oeis.org

39, 2835, 255191, 257233353, 2315100338, 1833559470601, 429052916136639, 123567239847463143, 56717363089986833887, 2586311756903401044465, 46553611624261219442817, 154185561699553158848604845
Offset: 1

Views

Author

Artur Jasinski, Oct 14 2008

Keywords

Comments

For denominators see A145620. For general properties of A_l(x) see A145609.

Crossrefs

Cf. A145609 - A145640.

Programs

  • Mathematica
    m = 6; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Numerator[k]], {r, 1, 25}]; aa (* Artur Jasinski *)
a[n_,m_]:=Integrate[(m-x^n)/(m-x),{x,0,1}]+(m^n-m)Log[m/(m-1)]
Table[6 a[2 n, 6] // FullSimplify  // Numerator, {n,1,25}]  (* Gerry Martens , Jun 04 2016 *)

Extensions

Edited by R. J. Mathar, Aug 21 2009

A145620 Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=6.

Original entry on oeis.org

1, 2, 5, 140, 35, 770, 5005, 40040, 510510, 646646, 323323, 29745716, 14300825, 12257850, 59246275, 29386152400, 7346538100, 77138650050, 475688341975, 24735793782700, 253541886272675, 21804602219450050, 10902301109725025
Offset: 1

Views

Author

Artur Jasinski, Oct 14 2008

Keywords

Comments

For numerators see A145619. For general properties of A_l(x) see A145609.

Crossrefs

Cf. A145609 - A145640.

Programs

  • Mathematica
    m = 6; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Denominator[k]], {r, 1, 30}]; aa (*Artur Jasinski*)

Extensions

Edited by R. J. Mathar, Aug 21 2009

A145622 Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=7.

Original entry on oeis.org

2, 12, 20, 40, 72, 792, 10296, 102960, 583440, 11085360, 3695120, 254963280, 1274816400, 11473347600, 332727080400, 20629078984800, 20629078984800, 20629078984800, 763275922437600, 763275922437600, 31294312819941600
Offset: 1

Views

Author

Artur Jasinski, Oct 14 2008

Keywords

Comments

For numerators see A145621. For general properties of A_l(x) see A145609.

Crossrefs

Cf. A145609 - A145640.

Programs

  • Mathematica
    m = 7; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Denominator[k]], {r, 1, 30}]; aa (*Artur Jasinski*)

Extensions

Edited by R. J. Mathar, Aug 21 2009

A145625 Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=9.

Original entry on oeis.org

171, 27819, 11267049, 12776837121, 1034923809573, 922117114354533, 970989321415598469, 31460054013865485891, 43320494377092775505339, 333351204231728907635493393, 27001447542770041518585314553
Offset: 1

Views

Author

Artur Jasinski, Oct 14 2008

Keywords

Comments

For denominators see A145626. For general properties of A_l(x) see A145609.

Crossrefs

Cf. A145609 - A145640.

Programs

  • Mathematica
    m = 9; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Numerator[k]], {r, 1, 25}]; aa (* Artur Jasinski *)
a[n_,m_]:=Integrate[(m-x^n)/(m-x),{x,0,1}]+(m^n-m)Log[m/(m-1)]
Table[9 a[2 n, 9] // Simplify  // Numerator, {n,1,25}]  (* Gerry Martens , Jun 04 2016 *)

Extensions

Edited by R. J. Mathar, Aug 21 2009

A145626 Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=9.

Original entry on oeis.org

2, 4, 20, 280, 280, 3080, 40040, 16016, 272272, 25865840, 25865840, 594914320, 2974571600, 2974571600, 86262576400, 5348279736800, 5348279736800, 5348279736800, 10415071066400, 10415071066400, 427017913722400
Offset: 1

Views

Author

Artur Jasinski, Oct 14 2008

Keywords

Comments

For numerators see A145625. For general properties of A_l(x) see A145609.

Crossrefs

Cf. A145609 - A145640.

Programs

  • Mathematica
    m = 9; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Denominator[k]], {r, 1, 30}]; aa (*Artur Jasinski*)

Extensions

Edited by R. J. Mathar, Aug 21 2009

A145627 Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=10.

Original entry on oeis.org

105, 63215, 1053605, 2950094435, 663771248638, 1460296747017355, 135598983651622355, 108479186921297959075, 15367884813850544296195, 29198981146316034164367667, 3406547800403537319177914415
Offset: 1

Views

Author

Artur Jasinski, Oct 14 2008

Keywords

Comments

For denominators see A145629. For general properties of A_l(x) see A145609.

Crossrefs

Cf. A145609 - A145640.

Programs

  • Mathematica
    m = 10; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Numerator[k]], {r, 1, 25}]; aa (* Artur Jasinski *)
a[n_,m_]:=Integrate[(m-x^n)/(m-x),{x,0,1}]+(m^n-m)Log[m/(m-1)]
Table[10 a[2 n, 10] // FullSimplify // Numerator, {n,1,25}] (* Gerry Martens , Jun 04 2016*)

Extensions

Edited by R. J. Mathar, Aug 21 2009

A145628 Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=11.

Original entry on oeis.org

253, 184195, 111439537, 188778591353, 68526628697791, 8291722072462741, 13042878819984222253, 3156376674436182358799, 6492666819315227120658143, 2985328203521141430107897005, 361224712626058113043082041693
Offset: 1

Views

Author

Artur Jasinski, Oct 14 2008

Keywords

Comments

For denominators see A145630. For general properties of A_l(x) see A145609.

Crossrefs

Cf. A145609 - A145640.

Programs

  • Mathematica
    m = 11; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Numerator[k]], {r, 1, 25}]; aa (* Artur Jasinski *)
a[n_,m_]:=Integrate[(m-x^n)/(m-x),{x,0,1}]+(m^n-m)Log[m/(m-1)]
Table[11 a[2 n, 11] // FullSimplify // Numerator, {n,1,25}] (* Gerry Martens , Jun 04 2016*)

Extensions

Edited by R. J. Mathar, Aug 21 2009
Previous Showing 21-30 of 40 results. Next

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

Content is available under The OEIS End-User License Agreement.