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.

A371612 G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^2) )^2.

Original entry on oeis.org

1, 2, 3, 12, 49, 218, 1037, 5106, 25909, 134410, 709691, 3801498, 20606654, 112828202, 623087675, 3466539248, 19411070496, 109313442562, 618713495451, 3517737628368, 20081523836403, 115058714898196, 661432784830204, 3813891082337178, 22052422636145522
Offset: 0

Views

Author

Seiichi Manyama, Mar 29 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n, r=2, s=1, t=0, u=4) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

Formula

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

A378411 G.f. A(x) satisfies A(x) = ( 1 + x * (1 + x*A(x)^(3/2)) )^2.

Original entry on oeis.org

1, 2, 3, 8, 19, 50, 137, 380, 1088, 3152, 9270, 27576, 82794, 250700, 764454, 2345688, 7237318, 22438988, 69876356, 218456216, 685400835, 2157396738, 6810801959, 21559694364, 68417766207, 217617573110, 693655532081, 2215401956720, 7088605614314, 22720370822508
Offset: 0

Views

Author

Seiichi Manyama, Dec 08 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n, r=2, s=1, t=0, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Formula

a(n) = 2 * Sum_{k=0..n} binomial(3*(n-k)+2,k) * binomial(k,n-k)/(3*(n-k)+2).
G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A019497.

A378787 G.f. A(x) satisfies A(x) = ( 1 + x * (1 + x*A(x)^2)^3 )^2.

Original entry on oeis.org

1, 2, 7, 36, 197, 1184, 7425, 48308, 322521, 2198064, 15227850, 106924154, 759245463, 5442675080, 39335090088, 286296369000, 2096706604597, 15439417451928, 114243931954962, 849030345258990, 6334510149389409, 47428709540589036, 356261301882333885
Offset: 0

Views

Author

Seiichi Manyama, Dec 07 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n, r=2, s=3, t=0, u=4) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Formula

a(n) = Sum_{k=0..n} binomial(4*(n-k)+2,k) * binomial(3*k,n-k)/(2*(n-k)+1).
G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A137957.
Showing 1-3 of 3 results.