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 1-3 of 3 results.

A366089 Expansion of (1/x) * Series_Reversion( x*(1-x)^3/(1-x-x^4) ).

Original entry on oeis.org

1, 2, 7, 30, 142, 715, 3756, 20349, 112864, 637659, 3656775, 21229923, 124531256, 736920158, 4393859967, 26371222935, 159193382812, 965923527255, 5887659026592, 36034716884127, 221362690616841, 1364404640452602, 8435444693847402
Offset: 0

Views

Author

Seiichi Manyama, Sep 28 2023

Keywords

Crossrefs

Programs

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

Formula

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

A366054 Expansion of (1/x) * Series_Reversion( x*(1-x)^2/(1-x+x^4) ).

Original entry on oeis.org

1, 1, 2, 5, 15, 49, 168, 594, 2149, 7919, 29627, 112254, 429884, 1661308, 6470678, 25375070, 100106145, 397018815, 1582005849, 6330533220, 25428891084, 102497788194, 414445390730, 1680617637425, 6833083703094, 27849689394894, 113762630541908
Offset: 0

Views

Author

Seiichi Manyama, Sep 27 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n\4, binomial(n+1, k)*binomial(2*n-3*k, n-4*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+1,k) * binomial(2*n-3*k,n-4*k).

A366056 Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1-x+x^4) ).

Original entry on oeis.org

1, 3, 15, 91, 613, 4408, 33143, 257400, 2048825, 16625940, 137033316, 1144010387, 9653706723, 82208879366, 705587243802, 6097408839400, 53007770199641, 463269048213536, 4067950092964440, 35871913838983980, 317533385082542404, 2820492099258807887
Offset: 0

Views

Author

Seiichi Manyama, Sep 27 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n\4, binomial(n+1, k)*binomial(4*n-3*k+2, n-4*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+1,k) * binomial(4*n-3*k+2,n-4*k).
Showing 1-3 of 3 results.