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.

A379331 G.f. A(x) satisfies A(x) = 1/sqrt( (1 - 2*x*A(x)^3) * (1 - 2*x*A(x)) ).

Original entry on oeis.org

1, 2, 12, 100, 976, 10432, 118216, 1395200, 16965664, 211078656, 2674095616, 34378044416, 447359023072, 5881178595328, 77992591652992, 1042089880305664, 14015275654390272, 189583355671740416, 2577607282441795840, 35205701425533550592, 482822120552883164160
Offset: 0

Views

Author

Seiichi Manyama, Dec 21 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 2^n*sum(k=0, n, binomial(n/2+2*k+1/2, k)*binomial(3*n/2-1/2, n-k)/(n+4*k+1));

Formula

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

A379329 G.f. A(x) satisfies A(x) = 1/sqrt( (1 - 2*x) * (1 - 2*x*A(x)) ).

Original entry on oeis.org

1, 2, 6, 22, 92, 420, 2034, 10262, 53330, 283410, 1532698, 8406698, 46650072, 261416000, 1477208374, 8407900890, 48158339716, 277375020772, 1605477915982, 9333727605762, 54478721494436, 319120526072380, 1875410643820166, 11054224586789010, 65334486288626586, 387118590382759994
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(3*n/2-3*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(3*n/2-3*k/2-1/2,n-k)/(n+k+1).

A379382 G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x))/(1 - 2*x*A(x)^2) ).

Original entry on oeis.org

1, 2, 8, 48, 336, 2560, 20608, 172416, 1484288, 13062144, 116977664, 1062600704, 9767067648, 90673700864, 848971661312, 8007542571008, 76014137180160, 725681289822208, 6962697126019072, 67105309925048320, 649362348326256640, 6306663216709632000
Offset: 0

Views

Author

Seiichi Manyama, Dec 22 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 2^n*sum(k=0, n, binomial(n/2+3*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+3*k/2-1/2,k) * binomial(n/2+k/2+1/2,n-k)/(n+k+1).
a(n) = 2^n * A106228(n).
Showing 1-3 of 3 results.