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.

A369502 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2+x)^2 ).

Original entry on oeis.org

1, 6, 47, 420, 4059, 41316, 436345, 4737018, 52535950, 592667532, 6779699073, 78458218746, 916886214115, 10805128064100, 128260666769895, 1532180536574580, 18405744106135914, 222204347510440092, 2694506677864591810, 32804976554127379680, 400837173223351237295
Offset: 0

Views

Author

Seiichi Manyama, Jan 25 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2+x)^2)/x)
    
  • PARI
    a(n) = sum(k=0, n, binomial(2*n+2, k)*binomial(4*n-2*k+4, n-k))/(n+1);

Formula

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

A369503 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2+x^2)^2 ).

Original entry on oeis.org

1, 4, 24, 168, 1284, 10384, 87360, 756704, 6703168, 60444928, 552990592, 5120101760, 47887472000, 451759449600, 4293634467840, 41073654689280, 395170166443008, 3821262491103232, 37118973530660864, 362035991963869184, 3544080121528001536
Offset: 0

Views

Author

Seiichi Manyama, Jan 25 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2+x^2)^2)/x)
    
  • PARI
    a(n) = sum(k=0, n\2, binomial(2*n+2, k)*binomial(4*n-2*k+4, n-2*k))/(n+1);

Formula

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

A369507 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x^3)^2 ).

Original entry on oeis.org

1, 6, 51, 508, 5535, 63888, 767689, 9502254, 120324606, 1551362160, 20296839585, 268785905790, 3595951246855, 48528885742200, 659856371680971, 9031161933443468, 124319953470044970, 1720113658097639532, 23908612149570793386, 333680424238179500976
Offset: 0

Views

Author

Seiichi Manyama, Jan 25 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3+x^3)^2)/x)
    
  • PARI
    a(n) = sum(k=0, n\3, binomial(2*n+2, k)*binomial(6*n-3*k+6, n-3*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+2,k) * binomial(6*n-3*k+6,n-3*k).
Showing 1-3 of 3 results.