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.

A381572 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x*A(x)))^2.

Original entry on oeis.org

1, 2, 7, 38, 267, 2232, 21200, 222556, 2536661, 31010886, 403097573, 5535291884, 79900803514, 1207657432714, 19052200105025, 312909670649562, 5338325737985841, 94422672774323512, 1728653714036740230, 32708138881741705812, 638762549199936808759, 12859693257887577375744
Offset: 0

Views

Author

Seiichi Manyama, Feb 28 2025

Keywords

Crossrefs

Column k=1 of A381571.
Cf. A381029.

Programs

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

Formula

See A381571.
G.f.: B(x)^2, where B(x) is the g.f. of A381029.

A381615 G.f. A(x) satisfies A(x) = 1/(1 - x * A(x*A(x)^3)^3).

Original entry on oeis.org

1, 1, 4, 31, 320, 3969, 56080, 876204, 14860614, 270231265, 5223002719, 106613106181, 2287120272173, 51367948203527, 1204141944566399, 29385603693050274, 744943334951904519, 19580887642660810193, 532781828387893449124, 14984377196395037979472
Offset: 0

Views

Author

Seiichi Manyama, Mar 01 2025

Keywords

Crossrefs

Programs

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

Formula

Let a(n,k) = [x^n] A(x)^k.
a(n,0) = 0^n; a(n,k) = k * Sum_{j=0..n} binomial(3*n-2*j+k,j)/(3*n-2*j+k) * a(n-j,3*j).

A381649 G.f. A(x) satisfies A(x) = 1 + x * A(x)^2 * A(x*A(x)^3)^3.

Original entry on oeis.org

1, 1, 5, 44, 510, 7024, 109362, 1871530, 34590180, 682396379, 14251399805, 313170119013, 7207845252630, 173129413258492, 4327373963163746, 112289379643018983, 3018922654575996866, 83951253980821314446, 2411137697712963195801, 71427857356498491780290
Offset: 0

Views

Author

Seiichi Manyama, Mar 03 2025

Keywords

Crossrefs

Column k=1 of A381648.

Programs

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

Formula

See A381648.
Showing 1-3 of 3 results.