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.

A369212 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2+x^3) ).

Original entry on oeis.org

1, 2, 5, 15, 50, 177, 652, 2473, 9594, 37892, 151846, 615859, 2523217, 10427471, 43415259, 181941198, 766841846, 3248517320, 13823977350, 59067577266, 253315964424, 1089998388418, 4704475230340, 20361365646315, 88351705071583, 384280788724692, 1675063399090659
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+1, k)*binomial(2*n-2*k+2, n-3*k))/(n+1);

Formula

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

A369159 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x^4) ).

Original entry on oeis.org

1, 3, 12, 55, 274, 1443, 7905, 44593, 257305, 1511553, 9010170, 54361486, 331336454, 2037132958, 12619056108, 78682008194, 493427982703, 3110202012353, 19693920616872, 125214061831251, 799059649687239, 5116372686471627, 32860439054510610
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+1, k)*binomial(3*n-3*k+3, n-4*k))/(n+1);

Formula

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

A371427 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 - x^4) ).

Original entry on oeis.org

1, 2, 5, 14, 41, 122, 363, 1066, 3046, 8300, 20791, 43738, 51297, -174406, -1825027, -10480330, -50143510, -218385772, -895007802, -3504952380, -13214355159, -48116028934, -169216483595, -573113441834, -1856620607526, -5675964306988, -15927363432481
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+1, k)*binomial(2*n-2*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(2*n-2*k+2,n-4*k).
Showing 1-3 of 3 results.