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.

A368931 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x-x^3) ).

Original entry on oeis.org

1, 2, 7, 31, 154, 819, 4560, 26244, 154874, 932074, 5698745, 35297535, 221016593, 1396717756, 8896798020, 57062237502, 368201804973, 2388587515239, 15568995139404, 101913055166811, 669678357109300, 4415837460391845, 29210203356645090
Offset: 0

Views

Author

Seiichi Manyama, Jan 10 2024

Keywords

Crossrefs

Programs

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

Formula

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

A368932 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x-x^4) ).

Original entry on oeis.org

1, 2, 7, 30, 144, 741, 3996, 22287, 127495, 743941, 4410555, 26492349, 160875186, 986007700, 6091548256, 37894543413, 237168491610, 1492323419929, 9434943086870, 59906035386393, 381832957589226, 2442251022673595, 15670578495195870
Offset: 0

Views

Author

Seiichi Manyama, Jan 10 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n\4, binomial(n+k, k)*binomial(3*n-3*k+1, n-4*k))/(n+1);
    
  • PARI
    my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x-x^4))/x)

Formula

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

A368937 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^5) ).

Original entry on oeis.org

1, 2, 7, 30, 143, 727, 3861, 21165, 118845, 680064, 3951291, 23247874, 138229486, 829292780, 5013767772, 30516496017, 186837457296, 1149894814718, 7110026033305, 44146396259805, 275139524189497, 1720647439298395, 10793938343564655, 67905034046934225
Offset: 0

Views

Author

Seiichi Manyama, Jan 10 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n\5, (-1)^k*binomial(n+k, k)*binomial(3*n-4*k+1, n-5*k))/(n+1);
    
  • PARI
    my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x+x^5))/x)

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/5)} (-1)^k * binomial(n+k,k) * binomial(3*n-4*k+1,n-5*k).
Showing 1-3 of 3 results.