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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A374868 Obverse convolution (2n+1)**A000032; see Comments.

Original entry on oeis.org

3, 10, 112, 1620, 39424, 1404000, 75841920, 6112753920, 742328893440, 136268470800000, 38081363493888000, 16296693648238080000, 10743612584546575319040, 10968661020433308192000000, 17425075496868344523423744000, 43253347261338355732569538560000
Offset: 0

Views

Author

Clark Kimberling, Aug 28 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Programs

  • Mathematica
    s[n_] := 2 n + 1; t[n_] := LucasL[n];
    u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
    Table[u[n], {n, 0, 20}]

A374869 Obverse convolution (2n+1)**(2^n); see Comments.

Original entry on oeis.org

2, 12, 150, 3528, 151470, 11835252, 1695534750, 450137811600, 223862873592150, 210586842089730540, 377818996488206253750, 1301732219036581449975000, 8661531388920997249932018750, 111817906864517248017080187253860, 2811403559627160557559224217577548750
Offset: 0

Views

Author

Clark Kimberling, Aug 28 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Programs

  • Mathematica
    s[n_] := 2 n + 1; t[n_] := 2^n;
    u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
    Table[u[n], {n, 0, 20}]

A374871 Obverse convolution (n)**(n!); see Comments.

Original entry on oeis.org

1, 2, 12, 216, 13440, 3600000, 5137292160, 46921886323200, 3202231533127925760, 1864324101234676309401600, 10395949648645451956665600000000, 615427797319269256611285148820828160000, 424360339875987535547553745155503616043253760000
Offset: 0

Views

Author

Clark Kimberling, Aug 28 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Programs

  • Mathematica
    s[n_] := n; t[n_] := n!;
    u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
    Table[u[n], {n, 0, 13}]

A374872 Obverse convolution (2n+1)**(n!); see Comments.

Original entry on oeis.org

2, 8, 72, 1680, 126000, 38811960, 61785091368, 616892274180000, 45374160012072012000, 28175746072918961153889000, 166250736077540332478371155891000, 10349136183590980028259106116944710102320, 7466148323412227422384379930251940448396455130000
Offset: 0

Views

Author

Clark Kimberling, Aug 28 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Programs

  • Mathematica
    s[n_] := 2 n + 1; t[n_] := n!;
    u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
    Table[u[n], {n, 0, 13}]

A374874 Obverse convolution (2^n)**(n!); see Comments.

Original entry on oeis.org

2, 6, 45, 1260, 183600, 176490600, 1331315425440, 90579563457377280, 62660380648301551779840, 490943560922866363260804710400, 47971283739623513755756038396090777600, 63754384387913077858449560360392597458596659200
Offset: 0

Views

Author

Clark Kimberling, Sep 11 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Programs

  • Mathematica
    s[n_] := 2^n; t[n_] := n!;
    u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
    Table[u[n], {n, 0, 13}]

A374875 Obverse convolution (n!)**A000045; see Comments.

Original entry on oeis.org

1, 2, 8, 108, 6048, 2016000, 4704480000, 90747697360320, 16354583259191654400, 30715766088740592418944000, 663127739407725552738699264000000, 179787972724005939376371515117626982400000, 664012371757346621597356008815791014131773440000000
Offset: 0

Views

Author

Clark Kimberling, Sep 12 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Programs

  • Mathematica
    s[n_] := n!; t[n_] := Fibonacci[n];
    u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
    Table[u[n], {n, 0, 13}]

A374876 Obverse convolution (n!)**A000032; see Comments.

Original entry on oeis.org

3, 6, 32, 480, 36400, 15811200, 48402042480, 1206043046666640, 276580685164781030400, 652981562430940302718878720, 17542316699101442389453162362832320, 5863769800904933880463358889014242882022400, 26512736336116399269871416473897490370043694674400000
Offset: 0

Views

Author

Clark Kimberling, Sep 13 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Programs

  • Mathematica
    s[n_] := n!; t[n_] := LucasL[n];
    u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
    Table[u[n], {n, 0, 13}]

A374879 Obverse convolution (n)**(floor(3n/2)); see Comments.

Original entry on oeis.org

0, 1, 12, 144, 2400, 44100, 1016064, 25401600, 752716800, 23851713600, 865728864000, 33243988377600, 1429216756531200, 64493406138470400, 3205589417533440000, 166232708366376960000, 9379957624086763929600, 549606892036333824000000, 34710813126114757632000000
Offset: 0

Views

Author

Clark Kimberling, Sep 13 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.
If k>=0, then a(2k+1) is a square.

Crossrefs

Programs

  • Mathematica
    s[n_] := n; t[n_] := Floor[3 n/2];
    u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
    Table[u[n], {n, 0, 24}]

Formula

a(n) ~ 3^(3*n) * n^(n+1) / (2^(3*n) * exp(n)). - Vaclav Kotesovec, Sep 13 2024

A374884 Obverse convolution (n^2)**(n^2+1); see Comments.

Original entry on oeis.org

1, 4, 75, 3600, 314721, 42928704, 8362250379, 2196324000000, 746766466070625, 318799285706474496, 166848786507705952491, 105015062916733187395584, 78238953853457166762890625, 68086982534559349084416000000, 68431651668664224198422729187051
Offset: 0

Views

Author

Clark Kimberling, Sep 13 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Programs

  • Mathematica
    s[n_] := n^2; t[n_] := n^2 + 1;
    u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
    Table[u[n], {n, 0, 20}]

Formula

a(n) ~ exp((Pi-4)*n/2) * n^(2*n+2). - Vaclav Kotesovec, Sep 13 2024

A374885 Obverse convolution (n^2)**(n(n+1)/2); see Comments.

Original entry on oeis.org

0, 1, 24, 1080, 78400, 8415000, 1254839040, 248351295808, 63008824320000, 19941885512640000, 7702879929184000000, 3566623957287040742400, 1950112829958404302503936, 1243182598706645953527808000, 913988528405739663528960000000
Offset: 0

Views

Author

Clark Kimberling, Jul 31 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Programs

  • Mathematica
    s[n_] := n^2; t[n_] := n (n + 1)/2;
    u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
    Table[u[n], {n, 0, 20}]

Formula

a(n) ~ n^(2*n+2) / (2^((n+2)/3) * exp(2*n - (2*n+1)*Pi/(3*sqrt(2)))). - Vaclav Kotesovec, Jul 31 2024
Previous Showing 31-40 of 58 results. Next