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 1-10 of 13 results. Next

A015013 q-factorial numbers for q=-2.

Original entry on oeis.org

1, 1, -1, -3, 15, 165, -3465, -148995, 12664575, 2165642325, -738484032825, -504384594419475, 688484971382583375, 1880252456845835197125, -10268058666835106011499625, -112158004817839862963610403875, 2450091615245711806440069272649375, 107046952761700394535173066591323843125
Offset: 0

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Column k=2 of A384454.
Cf. A001045, A330862.

Programs

  • Magma
    I:=[1]; [n le 1 select I[n] else (((-2)^n - 1) * Self(n-1))/(-3): n in [1..18]]; // Vincenzo Librandi, Oct 26 2012
  • Mathematica
    RecurrenceTable[{a[1]==1, a[n]==(((-2)^n - 1) * a[n-1])/(-3)}, a, {n, 15}]
Table[QFactorial[n, -2], {n, 20}] (* Vladimir Reshetnikov, Sep 16 2016 *)
  • PARI
    a(n) = prod(k=1, n, ((-2)^k-1)/(-3)) \\ Michel Marcus, Apr 05 2016

Formula

a(n) = Product_{k=1..n} ((-2)^k - 1) / (-2 - 1).
a(1) = 1, a(n) = (((-2)^n - 1) * a(n-1))/(-3). - Vincenzo Librandi, Oct 26 2012
a(n) = (-1)^(floor((n mod 4)/2)) * Product_{k=1..n} A001045(k). - Altug Alkan, Apr 05 2016
a(n) ~ (-1)^floor(n/2) * c * 2^(n*(n+1)/2) / 3^n, where c = Product_{k>=1} (1 - 1/(-2)^k) = 1.21072413030105918013... (A330862). - Amiram Eldar, Aug 09 2025

Extensions

a(0)=1 prepended by Seiichi Manyama, May 30 2025

A015015 q-factorial numbers for q=-3.

Original entry on oeis.org

1, 1, -2, -14, 280, 17080, -3108560, -1700382320, 2788627004800, 13722833490620800, -202576467988544249600, -8971504037808659182035200, 1191954026463258458925196672000, 475090227821752019816863814722432000, -568085339196037403679856371543830284544000, -2037851067068183667490280132124059680133919488000
Offset: 0

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Column k=3 of A384454.
Cf. A015001.

Programs

  • Magma
    [n le 1 select 1 else ((-3)^n - 1)*Self(n-1)/(-4): n in [1..18]]; // Vincenzo Librandi, Oct 26 2012
  • Mathematica
    RecurrenceTable[{a[1]==1, a[n]==(((-3)^n - 1) * a[n-1])/(-4)}, a, {n, 18}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-3)^k - 1)/(-3 - 1).
a(1) = 1, a(n) = ((-3)^n - 1)*a(n-1)/(-4). - Vincenzo Librandi, Oct 26 2012
a(n) ~ (-1)^floor(n/2) * c * 3^(n*(n+1)/2) / 4^n, where c = Product_{k>=1} (1 - 1/(-3)^k) = 1.2176479365615020492... . - Amiram Eldar, Aug 09 2025

Extensions

a(0)=1 prepended by Seiichi Manyama, May 30 2025

A015017 q-factorial numbers for q=-4.

Original entry on oeis.org

1, 1, -3, -39, 1989, 407745, -333943155, -1094331718935, 14343405840081045, 752010424789609108305, -157707866234752874148183075, -132294978377551030760819002477575, 443908259132104963309174796130361690725, 5958035886896289829709072930982993020807155425
Offset: 0

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Column k=4 of A384454.
Cf. A015002.

Programs

  • Magma
    [n le 1 select 1 else ((-4)^n - 1)*Self(n-1)/(-5): n in [1..18]]; // Vincenzo Librandi, Oct 26 2012
  • Mathematica
    RecurrenceTable[{a[1]==1, a[n]==(((-4)^n-1) * a[n-1])/(-5)}, a, {n, 18}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-4)^k - 1) / (-4 - 1).
a(1) = 1, a(n) = ((-4)^n - 1)*a(n-1)/(-5). - Vincenzo Librandi, Oct 26 2012
a(n) ~ (-1)^floor(n/2) * c * 4^(n*(n+1)/2) / 5^n, where c = Product_{k>=1} (1 - 1/(-4)^k) = 1.1864623436704848646... . - Amiram Eldar, Aug 09 2025

Extensions

a(0)=1 prepended by Seiichi Manyama, May 30 2025

A015018 q-factorial numbers for q=-5.

Original entry on oeis.org

1, 1, -4, -84, 8736, 4551456, -11851991424, -154324780331904, 10047160498728278016, 3270561732706527788046336, -5323179358400075453935368658944, -43320145405426340445710562789228109824, 1762701221841919957075369153792221868461981696, 358622481951075194907281490606356664886183644743663616
Offset: 0

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Column k=5 of A384454.
Cf. A015004.

Programs

  • Magma
    [n le 1 select 1 else ((-5)^n - 1)*Self(n-1)/(-6): n in [1..18]]; // Vincenzo Librandi, Oct 26 2012
  • Mathematica
    RecurrenceTable[{a[1]==1, a[n]==(((-5)^n - 1) * a[n-1])/(-6)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-5)^k - 1) / (-5 - 1).
a(1) = 1, a(n) = ((-5)^n - 1)*a(n-1)/(-6). - Vincenzo Librandi, Oct 26 2012
a(n) ~ (-1)^floor(n/2) * c * 5^(n*(n+1)/2) / 6^n, where c = Product_{k>=1} (1 - 1/(-5)^k) = 1.1596671959367684201... . - Amiram Eldar, Aug 09 2025

Extensions

a(0)=1 prepended by Seiichi Manyama, May 30 2025

A015019 q-factorial numbers for q=-6.

Original entry on oeis.org

1, 1, -5, -155, 28675, 31857925, -212333070125, -8491411807368875, 2037471806119124711875, 2933289072587326393069793125, -25337824341236140066496699758578125, -1313212585969062194023540996089250607796875, 408368279891017634352398087776483543777178681171875
Offset: 0

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Column k=6 of A384454.
Cf. A015005.

Programs

  • Magma
    [n le 1 select 1 else ((-6)^n - 1)*Self(n-1)/(-7): n in [1..18]]; // Vincenzo Librandi, Oct 26 2012
  • Mathematica
    RecurrenceTable[{a[1]==1, a[n]==(((-6)^n - 1) * a[n-1])/(-7)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-6)^k - 1) / (-6 - 1).
a(1) = 1, a(n) = ((-6)^n - 1)*a(n-1)/(-7). - Vincenzo Librandi, Oct 26 2012
a(n) ~ (-1)^floor(n/2) * c * 6^(n*(n+1)/2) / 7^n, where c = Product_{k>=1} (1 - 1/(-6)^k) = 1.1387567153634922027... . - Amiram Eldar, Aug 09 2025

Extensions

a(0)=1 prepended by Seiichi Manyama, May 30 2025

A015020 q-factorial numbers for q=-7.

Original entry on oeis.org

1, 1, -6, -258, 77400, 162617400, -2391451484400, -246183190158589200, 177399606828279377520000, 894839274162813664365761520000, -31596243236160097777438406008857120000, -7809512095098558650122990001755435531352160000, 13511712475016607822799577492128185918816231362544000000
Offset: 0

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Column k=7 of A384454.
Cf. A015006.

Programs

  • Magma
    [n le 1 select 1 else ((-7)^n - 1)*Self(n-1)/(-8): n in [1..13]]; // Vincenzo Librandi, Oct 26 2012
  • Mathematica
    RecurrenceTable[{a[1]==1, a[n]==(((-7)^n - 1) * a[n-1])/(-8)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-7)^k - 1) / (-7 - 1).
a(1) = 1, a(n) = ((-7)^n - 1)*a(n-1)/(-8). - Vincenzo Librandi, Oct 26 2012
a(n) ~ (-1)^floor(n/2) * c * 7^(n*(n+1)/2) / 8^n, where c = Product_{k>=1} (1 - 1/(-7)^k) = 1.1223882662358546529... . - Amiram Eldar, Aug 09 2025

Extensions

a(0)=1 prepended by Seiichi Manyama, May 30 2025

A015022 q-factorial numbers for q=-8.

Original entry on oeis.org

1, 1, -7, -399, 181545, 661005345, -19253102683815, -4486300228074519855, 8363069275661695069900425, 124719129516554187174725699959425, -14879571721119777957252576955487113947975, -14201616428474592152386976225370375696382583866575
Offset: 0

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Column k=8 of A384454.
Cf. A015007.

Programs

  • Magma
    [n le 1 select 1 else ((-8)^n - 1)*Self(n-1)/(-9): n in [1..13]]; // Vincenzo Librandi, Oct 26 2012
  • Mathematica
    RecurrenceTable[{a[1]==1, a[n]==(((-8)^n - 1) * a[n-1])/(-9)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-8)^k - 1) / (-8 - 1).
a(1) = 1, a(n) = ((-8)^n - 1)*a(n-1)/(-9). - Vincenzo Librandi, Oct 26 2012
a(n) ~ (-1)^floor(n/2) * c * 8^(n*(n+1)/2) / 9^n, where c = Product_{k>=1} (1 - 1/(-8)^k) = 1.1093440055701933033... . - Amiram Eldar, Aug 09 2025

Extensions

a(0)=1 prepended by Seiichi Manyama, May 30 2025

A015023 q-factorial numbers for q=-9.

Original entry on oeis.org

1, 1, -8, -584, 383104, 2262229120, -120223904353280, -57502732780460764160, 247530403723531598578155520, 9589835030046843645163231485460480, -3343768718134086569119429099709242848051200, -10493100546581905859843718978714438348266087953203200
Offset: 0

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Column k=9 of A384454.
Cf. A015008.

Programs

  • Magma
    I:=[1]; [n le 1 select I[n] else (((-9)^n - 1) * Self(n-1))/(-10): n in [1..13]]; // Vincenzo Librandi, Oct 26 2012
  • Mathematica
    RecurrenceTable[{a[1]==1, a[n]==(((-9)^n - 1) * a[n-1])/(-10)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-9)^k - 1) / (-9 - 1).
a(1) = 1, a(n) = (((-9)^n - 1) * a(n-1))/(-10). - Vincenzo Librandi, Oct 26 2012
a(n) ~ (-1)^floor(n/2) * c * 9^(n*(n+1)/2) / 10^n, where c = Product_{k>=1} (1 - 1/(-9)^k) = 1.098748287932263023... . - Amiram Eldar, Aug 09 2025

Extensions

a(0)=1 prepended by Seiichi Manyama, May 30 2025

A015025 q-factorial numbers for q=-10.

Original entry on oeis.org

1, 1, -9, -819, 744471, 6767985861, -615270826637649, -559337171058846967059, 5084883322413411422459366631, 462262120681663158624798004859942421, -420238291486760860506028808179511473194550689, -3820348104463302212917240152587016011603143670290413699
Offset: 0

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Column k=10 of A384454.
Cf. A015009.

Programs

  • Magma
    [n le 1 select 1 else ((-10)^n - 1)*Self(n-1)/(-11): n in [1..13]]; // Vincenzo Librandi, Oct 26 2012
  • Mathematica
    RecurrenceTable[{a[1]==1, a[n]==(((-10)^n - 1) * a[n-1])/(-11)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-10)^k - 1) / (-10 - 1).
a(1) = 1, a(n) = ((-10)^n - 1)*a(n-1)/(-11). - Vincenzo Librandi, Oct 26 2012
a(n) ~ (-1)^floor(n/2) * c * 10^(n*(n+1)/2) / 11^n, where c = Product_{k>=1} (1 - 1/(-10)^k) = 1.0899898999990010... . - Amiram Eldar, Aug 10 2025

Extensions

a(0)=1 prepended by Seiichi Manyama, May 30 2025

A015026 q-factorial numbers for q=-11.

Original entry on oeis.org

1, 1, -10, -1110, 1354200, 18174718200, -2683133647866000, -4357223907912681246000, 77834136400782124140797040000, 15294068523753116384387488625702640000, -33057395763506647102922925284376653918412000000, -785971734280677729025139143429963192709390305509012000000
Offset: 0

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Column k=11 of A384454.
Cf. A015011.

Programs

  • Magma
    [n le 1 select 1 else ((-11)^n - 1)*Self(n-1)/(-12): n in [1..13]]; // Vincenzo Librandi, Oct 26 2012
  • Mathematica
    RecurrenceTable[{a[1]==1, a[n]==(((-11)^n - 1) a[n-1])/(-12)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-11)^k - 1) / (-11 - 1).
a(1) = 1, a(n) = ((-11)^n - 1) * a(n-1)/(-12). - Vincenzo Librandi, Oct 26 2012
a(n) ~ (-1)^floor(n/2) * c * 11^(n*(n+1)/2) / 12^n, where c = Product_{k>=1} (1 - 1/(-11)^k) = 1.08263836756981274767... . - Amiram Eldar, Aug 10 2025

Extensions

a(0)=1 prepended by Seiichi Manyama, May 30 2025
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