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 1-5 of 5 results.

A366095 Expansion of (1/x) * Series_Reversion( x*(1+x-x^3)/(1+x)^2 ).

Original entry on oeis.org

1, 1, 1, 2, 5, 11, 25, 63, 162, 415, 1085, 2896, 7795, 21127, 57785, 159253, 441351, 1229506, 3442150, 9678358, 27315923, 77364683, 219815829, 626375327, 1789627564, 5125729137, 14714078483, 42327358520, 121998755959, 352272227623, 1018915014521
Offset: 0

Views

Author

Seiichi Manyama, Sep 29 2023

Keywords

Crossrefs

Cf. A366071, A366096, A366097.

Programs

  • PARI
    a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(n-k+1, n-3*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(n-k+1,n-3*k).

A366096 Expansion of (1/x) * Series_Reversion( x*(1+x-x^3)/(1+x)^3 ).

Original entry on oeis.org

1, 2, 5, 15, 51, 187, 719, 2858, 11650, 48438, 204630, 875867, 3790172, 16554305, 72883035, 323109570, 1441152303, 6462494515, 29118219850, 131761291852, 598529262016, 2728346941040, 12476533435028, 57220220120080, 263125059775970, 1212942573227309
Offset: 0

Views

Author

Seiichi Manyama, Sep 29 2023

Keywords

Crossrefs

Cf. A366071, A366095, A366097.

Programs

  • PARI
    a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(2*n-k+2, n-3*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(2*n-k+2,n-3*k).

A366097 Expansion of (1/x) * Series_Reversion( x*(1+x-x^3)/(1+x)^4 ).

Original entry on oeis.org

1, 3, 12, 56, 287, 1564, 8896, 52217, 313955, 1923775, 11970066, 75427608, 480365740, 3086989128, 19992893796, 130363352003, 855099212950, 5638480905533, 37354602517624, 248515024509486, 1659620048332369, 11121368629141886, 74759777174598964
Offset: 0

Views

Author

Seiichi Manyama, Sep 29 2023

Keywords

Crossrefs

Cf. A366071, A366095, A366096.

Programs

  • PARI
    a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(3*n-k+3, n-3*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(3*n-k+3,n-3*k).

A366101 Expansion of (1/x) * Series_Reversion( x*(1+x-x^5)/(1+x) ).

Original entry on oeis.org

1, 0, 0, 0, 0, 1, -1, 1, -1, 1, 5, -12, 20, -29, 39, 1, -109, 305, -611, 1051, -1145, 139, 3055, -9924, 22424, -37574, 43476, -14035, -97831, 368715, -852385, 1470767, -1823523, 885634, 3444224, -14239745, 34089723, -61051093, 80200515, -48234695, -123155951
Offset: 0

Views

Author

Seiichi Manyama, Sep 29 2023

Keywords

Crossrefs

Cf. A366071, A366102.

Programs

  • PARI
    a(n) = sum(k=0, n\5, (-1)^(n-k)*binomial(n+k, k)*binomial(n-4*k-1, n-5*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/5)} (-1)^(n-k) * binomial(n+k,k) * binomial(n-4*k-1,n-5*k).

A366102 Expansion of (1/x) * Series_Reversion( x*(1+x+x^4)/(1+x) ).

Original entry on oeis.org

1, 0, 0, 0, -1, 1, -1, 1, 4, -10, 17, -25, -1, 76, -217, 443, -490, -94, 1999, -6208, 11527, -12350, -4471, 63826, -184055, 332713, -342399, -231390, 2101215, -5790892, 10230983, -9625472, -10237792, 71714387, -190381165, 324440310, -275119412, -430340403
Offset: 0

Views

Author

Seiichi Manyama, Sep 29 2023

Keywords

Crossrefs

Cf. A366071, A366101.

Programs

  • PARI
    a(n) = sum(k=0, n\4, (-1)^(n-k)*binomial(n+k, k)*binomial(n-3*k-1, n-4*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (-1)^(n-k) * binomial(n+k,k) * binomial(n-3*k-1,n-4*k).
Showing 1-5 of 5 results.

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

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