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.

A369161 Expansion of (1/x) * Series_Reversion( x * ((1-x)^3-x^4) ).

Original entry on oeis.org

1, 3, 15, 91, 613, 4410, 33190, 258129, 2058281, 16737259, 138268611, 1157197639, 9790774861, 83606543660, 719638883748, 6237175439640, 54386540912490, 476782443732437, 4199713449255749, 37151346765537606, 329914740292813170, 2939975733035070000
Offset: 0

Views

Author

Seiichi Manyama, Jan 15 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3-x^4))/x)
    
  • PARI
    a(n) = sum(k=0, n\4, binomial(n+k, k)*binomial(4*n-k+2, n-4*k))/(n+1);

Formula

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

A369214 Expansion of (1/x) * Series_Reversion( x * ((1-x)^2-x^3) ).

Original entry on oeis.org

1, 2, 7, 31, 155, 833, 4696, 27393, 163944, 1001022, 6211049, 39048685, 248213672, 1592561156, 10300192220, 67083304750, 439571860881, 2895898913453, 19169805142929, 127442939722175, 850536450459795, 5696270624620125, 38271171118343550
Offset: 0

Views

Author

Seiichi Manyama, Jan 16 2024

Keywords

Crossrefs

Programs

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

Formula

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

A371432 Expansion of (1/x) * Series_Reversion( x * ((1-x)^2 + x^4) ).

Original entry on oeis.org

1, 2, 7, 30, 142, 714, 3740, 20178, 111325, 625042, 3559101, 20502014, 119249277, 699330360, 4130235408, 24543145310, 146629131642, 880184547880, 5305961255490, 32107022363150, 194947974895960, 1187354222296110, 7252099548616320, 44408257163905050
Offset: 0

Views

Author

Seiichi Manyama, Mar 23 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^2+x^4))/x)
    
  • PARI
    a(n) = sum(k=0, n\4, (-1)^k*binomial(n+k, k)*binomial(3*n-2*k+1, n-4*k))/(n+1);

Formula

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