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.

A379252 G.f. A(x) satisfies A(x) = ( (1 + x*A(x))/(1 - x*A(x)^3) )^2.

Original entry on oeis.org

1, 4, 40, 572, 9552, 174004, 3352440, 67171500, 1385457568, 29220437860, 627287390664, 13661411796508, 301096488681200, 6703186665881876, 150517000234338072, 3404956079399106700, 77526315562007606080, 1775260286963982001860, 40857405217738915499880, 944584396250976659451388
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(2*n+5*k+1, k)*binomial(2*n+4*k+2, n-k)/(n+2*k+1));

Formula

G.f.: B(x)^2 where B(x) is the g.f. of A379253.
a(n) = Sum_{k=0..n} binomial(2*n+5*k+1,k) * binomial(2*n+4*k+2,n-k)/(n+2*k+1).

A379282 G.f. A(x) satisfies A(x) = 1/( (1 - x*A(x)^2) * (1 - x*A(x)) )^2.

Original entry on oeis.org

1, 4, 34, 376, 4743, 64710, 929906, 13865206, 212509079, 3327383632, 52994140217, 855842582128, 13982509284464, 230686414552016, 3837897905208588, 64314848237403878, 1084624929809399857, 18393856772155371200, 313487249756740510907, 5366521088581773011788
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2024

Keywords

Crossrefs

Programs

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

Formula

G.f.: B(x)^2 where B(x) is the g.f. of A379284.
a(n) = 2 * Sum_{k=0..n} binomial(2*n+3*k+2,k) * binomial(3*n+k+1,n-k)/(2*n+3*k+2).

A379279 G.f. A(x) satisfies A(x) = ( (1 + x*A(x)^2) * (1 + x*A(x)) )^2.

Original entry on oeis.org

1, 4, 30, 288, 3125, 36490, 447478, 5683186, 74105002, 986302778, 13344661479, 182998935930, 2537838036761, 35530970858236, 501523116910044, 7129275916213606, 101973703002773268, 1466574750062589956, 21194869324964207133, 307642575576365729486, 4482940969372057898247
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(2*n+2*k+2, k)*binomial(2*n+2*k+2, n-k)/(n+k+1));

Formula

G.f.: B(x)^2 where B(x) is the g.f. of A215715.
a(n) = Sum_{k=0..n} binomial(2*n+2*k+2,k) * binomial(2*n+2*k+2,n-k)/(n+k+1).
Showing 1-3 of 3 results.