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 1-4 of 4 results.

A366052 Expansion of (1/x) * Series_Reversion( x*(1-x)^3/(1-x+x^3) ).

Original entry on oeis.org

1, 2, 7, 31, 154, 819, 4559, 26226, 154664, 930040, 5680920, 35150493, 219850505, 1387717660, 8828668582, 56553846890, 364449091112, 2361118198094, 15369247139879, 100468188756849, 659271433474584, 4341140182940382, 28675590236716905
Offset: 0

Views

Author

Seiichi Manyama, Sep 27 2023

Keywords

Crossrefs

Cf. A049128, A114997, A366051, A366053.

Programs

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

Formula

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

A366086 Expansion of (1/x) * Series_Reversion( x/(1-x-x^4) ).

Original entry on oeis.org

1, -1, 1, -1, 0, 4, -14, 34, -65, 89, -29, -331, 1464, -4148, 9010, -14366, 9761, 38895, -215015, 674423, -1594973, 2829973, -2732465, -4812567, 36116257, -124617681, 316617081, -611942761, 735416371, 488457845, -6451021289, 24658985649, -66990721867, 139346533259
Offset: 0

Views

Author

Seiichi Manyama, Sep 28 2023

Keywords

Crossrefs

Cf. A366087, A366088, A366089, A366090.
Cf. A366051, A366057.

Programs

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

Formula

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

A366053 Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1-x+x^3) ).

Original entry on oeis.org

1, 3, 15, 92, 628, 4579, 34917, 275041, 2220472, 18275896, 152780718, 1293657534, 11072033677, 95629771059, 832460471465, 7296161486583, 64331378963164, 570228657335744, 5078345448484216, 45418278349485960, 407749837317844851, 3673300856466182388
Offset: 0

Views

Author

Seiichi Manyama, Sep 27 2023

Keywords

Crossrefs

Cf. A049128, A114997, A366051, A366052.

Programs

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

Formula

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

A366057 Expansion of (1/x) * Series_Reversion( x/(1-x+x^5) ).

Original entry on oeis.org

1, -1, 1, -1, 1, 0, -5, 20, -55, 125, -246, 406, -461, -144, 3004, -11978, 35113, -86293, 181663, -314603, 365922, 150023, -2696308, 10969573, -32970453, 82976409, -178372934, 314133884, -367436684, -179661091, 2923282216, -11972239216, 36369188841, -92517132841
Offset: 0

Views

Author

Seiichi Manyama, Sep 27 2023

Keywords

Crossrefs

Cf. A364522, A365702, A366051.

Programs

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

Formula

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

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

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