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.

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A203523 v(n)/A000178(n); v=A203521 and A000178=(superfactorials).

Original entry on oeis.org

1, 5, 140, 25200, 55036800, 951035904000, 222618484408320000, 440079343769868042240000, 12254449406615745504215040000000, 7909254579604123100510930935480320000000, 48073937540175558516708030362614204937011200000000
Offset: 1

Views

Author

Clark Kimberling, Jan 03 2012

Keywords

Comments

It is conjectured that every term of A203523 is an integer.

Crossrefs

Cf. A203522, A203523, A000040, A093883.

Programs

  • Mathematica
    f[j_] := Prime[j]; z = 15;
v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
d[n_] := Product[(i - 1)!, {i, 1, n}] (* A000178 *)
Table[v[n], {n, 1, z}]                (* A203521 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}]   (* A203522 *)
Table[v[n]/d[n], {n, 1, 20}]          (* A203523 *)

A203525 a(n) = v(n+1)/(8*v(n)), where v=A203524.

Original entry on oeis.org

1, 15, 504, 17280, 1108800, 59304960, 5613753600, 944393748480, 83547459072000, 18057977118720000, 2985679725841612800, 366843845931171840000, 71218197373471948800000, 22048551163610844364800000, 7384118713322835982417920000
Offset: 1

Views

Author

Clark Kimberling, Jan 03 2012

Keywords

Comments

See A093883 for a discussion and guide to related sequences.

Crossrefs

Cf. A000040, A093883, A203315, A203524, A203526.

Programs

  • Mathematica
    f[j_] := Prime[j + 1]; z = 17;
v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
d[n_] := Product[(i - 1)!, {i, 1, n}]    (* A000178 *)
Table[v[n], {n, 1, z}]                   (* A203524 *)
Table[v[n + 1]/(8 v[n]), {n, 1, z - 1}]  (* A203525 *)
Table[v[n]/d[n], {n, 1, 20}]             (* A203526 *)

Extensions

Definition corrected by Georg Fischer, Nov 26 2021

A203526 v(n)/A000178(n); v=A203524 and A000178=(superfactorials).

Original entry on oeis.org

1, 8, 480, 322560, 1857945600, 137339338752000, 90498933234597888000, 806410654352196092559360000, 151104996166246050391298219704320000, 278316545034703677313682486677538340864000000
Offset: 1

Views

Author

Clark Kimberling, Jan 03 2012

Keywords

Comments

It is conjectured that every term of A203526 is an integer.

Crossrefs

Cf. A203524, A203525, A093883, A203317.

Programs

  • Mathematica
    f[j_] := Prime[j + 1]; z = 17;
v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
d[n_] := Product[(i - 1)!, {i, 1, n}]    (* A000178 *)
Table[v[n], {n, 1, z}]                   (* A203524 *)
Table[v[n + 1]/(8 v[n]), {n, 1, z - 1}]  (* A203525 *)
Table[v[n]/d[n], {n, 1, 20}]             (* A203526 *)

A203528 a(n) = v(n+1)/v(n), where v=A203527.

Original entry on oeis.org

5, 70, 1512, 33150, 842688, 34594560, 1705017600, 68981673600, 3038555520000, 212396207063040, 16628926183833600, 985240084758930000, 61949330611480166400, 6155242080686899200000, 445283762978503737288000
Offset: 1

Views

Author

Clark Kimberling, Jan 03 2012

Keywords

Comments

See A093883 for a discussion and guide to related sequences.

Crossrefs

Cf. A203527, A203529, A018252, A093883, A203416.

Programs

  • Mathematica
    t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];
nonprime = Rest[Union[t]]              (* A018252 *)
f[j_] := nonprime[[j]]; z = 20;
v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
d[n_] := Product[(i - 1)!, {i, 1, n}]  (* A000178 *)
Table[v[n], {n, 1, z}]                 (* A203527 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}]    (* A203528 *)
Table[v[n]/d[n], {n, 1, 20}]           (* A203529 *)

Extensions

Definition corrected by Georg Fischer, Nov 26 2021

A203529 a(n) = A203527(n)/A000178(n-1); A000178 = (superfactorials).

Original entry on oeis.org

1, 5, 175, 44100, 60913125, 427756329000, 20552836095792000, 6952965728817588480000, 11895516181976215338950400000, 99606443887767729350960121600000000, 5830034964946921746536425070101217280000000
Offset: 1

Views

Author

Clark Kimberling, Jan 03 2012

Keywords

Comments

It is conjectured that every term is an integer.

Crossrefs

Cf. A000178, A203527, A203528, A018252, A093883, A203417.

Programs

  • Mathematica
    t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];
nonprime = Rest[Union[t]]              (* A018252 *)
f[j_] := nonprime[[j]]; z = 20;
v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
d[n_] := Product[(i - 1)!, {i, 1, n}]  (* A000178 *)
Table[v[n], {n, 1, z}]                 (* A203527 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}]    (* A203528 *)
Table[v[n]/d[n], {n, 1, 20}]           (* A203529 *)

A203532 v(n+1)/v(n), where v=A203530.

Original entry on oeis.org

10, 168, 3315, 76608, 2661120, 113667840, 4311354600, 178738560000, 11178747740160, 791853627801600, 44783640216315000, 2693449157020876800, 246209683227475968000, 17126298576096297588000, 1253392853589570355200000
Offset: 1

Views

Author

Clark Kimberling, Jan 03 2012

Keywords

Crossrefs

Cf. A203530, A203532, A002808, A093883, A203419.

Programs

  • Mathematica
    t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];
composite = Rest[Rest[Union[t]]]       (* A002808 *)
f[j_] := composite[[j]]; z = 20;
v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
d[n_] := Product[(i - 1)!, {i, 1, n}]  (* A000178 *)
Table[v[n], {n, 1, z}]                 (* A203530 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}]    (* A203532 *)
Table[v[n]/d[n], {n, 1, 20}]           (* A203533 *)

A203533 a(n) = A203530(n)/A000178(n-1); A000178 = (superfactorials).

Original entry on oeis.org

1, 10, 840, 464100, 1481407200, 32851686067200, 5186361382800998400, 4436556151786001058816000, 19667253420867342693731328000000, 605862171333980479840975997239296000000, 132207384898194165523202154782408753283072000000
Offset: 1

Views

Author

Clark Kimberling, Jan 03 2012

Keywords

Comments

It is conjectured that every term is an integer.

Crossrefs

Cf. A000178, A203530, A203532, A002808, A093883, A203420.

Programs

  • Mathematica
    t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];
composite = Rest[Rest[Union[t]]]       (* A002808 *)
f[j_] := composite[[j]]; z = 20;
v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
d[n_] := Product[(i - 1)!, {i, 1, n}]  (* A000178 *)
Table[v[n], {n, 1, z}]                 (* A203530 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}]    (* A203532 *)
Table[v[n]/d[n], {n, 1, 20}]           (* A203533 *)

A203581 Vandermonde sequence using x^2 + xy + y^2 applied to (2,3,...,n+1).

Original entry on oeis.org

1, 19, 19684, 2294583564, 51987957606172224, 354256491848971529923455168, 1043097707370582731107248079473888804864, 1807964167474441339593635811814833549204957259332698112
Offset: 1

Views

Author

Clark Kimberling, Jan 04 2012

Keywords

Comments

See A093883 for a discussion and guide to related sequences.

Programs

  • Mathematica
    f[j_] := j + 1; z = 12;
v[n_] := Product[Product[f[j]^2 + f[j] f[k] + f[k]^2,
{j, 1, k - 1}], {k, 2, n}]
Table[v[n], {n, 1, z}]          (* A203581 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203582 *)

A203583 Vandermonde sequence using x^2 - xy + y^2 applied to (2,3,...,n+1).

Original entry on oeis.org

1, 7, 1092, 8278452, 5432386430016, 486397992095118597312, 8639860170780148341061245616128, 41813829909128704365291419329747443010781184, 72587617701933252361662389738534944047336321767596936396800
Offset: 1

Views

Author

Clark Kimberling, Jan 04 2012

Keywords

Comments

See A093883 for a discussion and guide to related sequences.

Programs

  • Mathematica
    f[j_] := j + 1; z = 12;
v[n_] := Product[Product[f[j]^2 - f[j] f[k] + f[k]^2,
{j, 1, k - 1}], {k, 2, n}]
Table[v[n], {n, 1, z}]          (* A203583 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203584 *)

A203585 Vandermonde sequence using x^2 + y^2 applied to (2,3,...,n+1).

Original entry on oeis.org

1, 13, 6500, 262769000, 1500305882400000, 1885591784499143760000000, 753074404854223679800035840000000000, 130639388303516205847055577677763494400000000000000
Offset: 1

Views

Author

Clark Kimberling, Jan 04 2012

Keywords

Comments

See A093883 for a discussion and guide to related sequences.

Programs

  • Mathematica
    f[j_] := j + 1; z = 12;
v[n_] := Product[Product[f[j]^2 + f[k]^2, {j, 1, k - 1}], {k, 2, n}]
Table[v[n], {n, 1, z}]          (* A203585 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203586 *)
Previous Showing 41-50 of 115 results. Next

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