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.

A371365 Expansion of (1/x) * Series_Reversion( x * (1-4*x)^3 / (1-3*x) ).

Original entry on oeis.org

1, 9, 141, 2701, 57513, 1307553, 31083925, 763267077, 19208408721, 492817411705, 12842067417309, 338956669920189, 9042967461581753, 243464712274093713, 6606427290991922277, 180492205687604057013, 4960765361688213527073
Offset: 0

Views

Author

Seiichi Manyama, Mar 19 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-4*x)^3/(1-3*x))/x)
    
  • PARI
    a(n) = sum(k=0, n, 3^(n-k)*binomial(3*n+k+2, k)*binomial(3*n+1, n-k))/(n+1);

Formula

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

A371362 Expansion of (1/x) * Series_Reversion( x * (1-3*x)^2 / (1-2*x) ).

Original entry on oeis.org

1, 4, 31, 298, 3199, 36742, 441748, 5489554, 69945295, 908836768, 11996580199, 160418984656, 2168512922692, 29584600414168, 406823494817560, 5632906243123090, 78465351036084655, 1098851032467132484, 15461857967408794333, 218490450548650811914
Offset: 0

Views

Author

Seiichi Manyama, Mar 19 2024

Keywords

Crossrefs

Programs

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

Formula

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

A371385 Expansion of (1/x) * Series_Reversion( x * (1-3*x)^3 / (1-x) ).

Original entry on oeis.org

1, 8, 109, 1808, 33283, 653696, 13419460, 284479136, 6179728951, 136842057800, 3077436307141, 70095952722752, 1613743723323028, 37490308916974496, 877802418598193488, 20693109628871653184, 490732756789852308223, 11699199238845493854872
Offset: 0

Views

Author

Seiichi Manyama, Mar 20 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-3*x)^3/(1-x))/x)
    
  • PARI
    a(n) = sum(k=0, n, 2^k*binomial(3*n+k+2, k)*binomial(3*n+1, n-k))/(n+1);

Formula

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