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.

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).

A366087 Expansion of (1/x) * Series_Reversion( x*(1-x)/(1-x-x^4) ).

Original entry on oeis.org

1, 0, 0, 0, -1, -1, -1, -1, 3, 8, 14, 21, 7, -40, -134, -291, -389, -188, 710, 2906, 6285, 8931, 5477, -15250, -66359, -149426, -224524, -154288, 336695, 1605033, 3774375, 5887736, 4504451, -7603388, -40495514, -98834842, -159804251, -134317549, 173843349, 1050099387
Offset: 0

Views

Author

Seiichi Manyama, Sep 28 2023

Keywords

Crossrefs

Cf. A366086, A366088, A366089, A366090.

Programs

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

A366088 Expansion of (1/x) * Series_Reversion( x*(1-x)^2/(1-x-x^4) ).

Original entry on oeis.org

1, 1, 2, 5, 13, 35, 96, 264, 719, 1913, 4875, 11478, 22860, 26044, -77216, -793820, -4394125, -20304455, -85805571, -343282020, -1321898694, -4943906064, -18052305410, -64551823869, -226418611750, -779487689870, -2633172840764, -8717790419014
Offset: 0

Views

Author

Seiichi Manyama, Sep 28 2023

Keywords

Crossrefs

Cf. A366086, A366087, A366089, A366090.
Cf. A366054.

Programs

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

A366090 Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1-x-x^4) ).

Original entry on oeis.org

1, 3, 15, 91, 611, 4370, 32637, 251550, 1985895, 15976676, 130508070, 1079562159, 9024791689, 76124252326, 647089873598, 5537663661590, 47670889706375, 412524981860848, 3586502483999720, 31311765471265548, 274398528604427286
Offset: 0

Views

Author

Seiichi Manyama, Sep 28 2023

Keywords

Crossrefs

Cf. A366086, A366087, A366088, A366089.
Cf. A366056.

Programs

  • PARI
    a(n) = sum(k=0, n\4, (-1)^k*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)} (-1)^k * binomial(n+1,k) * binomial(4*n-3*k+2,n-4*k).
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.