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 1-2 of 2 results.

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).

A379327 G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x)^2) * (1 + 2*x*A(x)) ).

Original entry on oeis.org

1, 2, 6, 22, 88, 372, 1634, 7382, 34078, 160034, 762078, 3671178, 17858476, 87599696, 432804190, 2151867226, 10758455224, 54053627604, 272780539742, 1382047628514, 7027307040920, 35848334763884, 183417043984246, 941007480667474, 4839875674661214, 24950493967407850
Offset: 0

Views

Author

Seiichi Manyama, Dec 21 2024

Keywords

Crossrefs

Programs

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

Formula

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