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 1-5 of 5 results.

A380769 E.g.f. A(x) satisfies A(x) = exp(x / (1 - x*A(x)^2)) / (1 - x*A(x)^2).

Original entry on oeis.org

1, 2, 15, 244, 6097, 206806, 8882599, 462280960, 28279981825, 1989026203114, 158149907916031, 14028441592927180, 1373477000345414353, 147124479131269256254, 17115976784139798114775, 2149092237059821309705816, 289673905062350873773963393, 41719133895880374350508378322
Offset: 0

Views

Author

Seiichi Manyama, Feb 02 2025

Keywords

Crossrefs

Programs

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

Formula

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

A380727 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^3 / (1 - x*A(x)^3)) / (1 - x*A(x)^3).

Original entry on oeis.org

1, 2, 31, 988, 48533, 3240016, 274099723, 28110919712, 3389978711785, 470124480093184, 73718009095023191, 12897488652935429632, 2490884805057416903869, 526368104133213244928000, 120811269372167469194820547, 29928528196949304888405323776, 7959458742917430589011715194833
Offset: 0

Views

Author

Seiichi Manyama, Jan 31 2025

Keywords

Crossrefs

Programs

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

Formula

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

A380768 E.g.f. A(x) satisfies A(x) = exp(x * A(x) / (1 - x*A(x)^2)) / (1 - x*A(x)^2).

Original entry on oeis.org

1, 2, 19, 361, 10481, 411961, 20477185, 1232420449, 87148819441, 7083132622561, 650681345267801, 66674532650884753, 7540078499903430937, 932840158873518067537, 125332464410926005144241, 18173310946391976757487041, 2828702590649296770695135585, 470432341506749952275419504321
Offset: 0

Views

Author

Seiichi Manyama, Feb 02 2025

Keywords

Crossrefs

Programs

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

Formula

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

A380754 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2 / (1 - x * A(x)^2)) / (1 - x * A(x)^2)^2.

Original entry on oeis.org

1, 3, 49, 1585, 78093, 5201771, 437861149, 44607800385, 5338028587705, 734060947570867, 114078994869344841, 19773620424489710417, 3782330144139700656325, 791450463143064447635355, 179843077195936890250320373, 44102411207136266014669068961, 11609166496582801689148704120561
Offset: 0

Views

Author

Seiichi Manyama, Feb 01 2025

Keywords

Crossrefs

Cf. A380726.

Programs

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

Formula

a(n) = n! * Sum_{k=0..n} (2*n+1)^(k-1) * binomial(5*n+1,n-k)/k!.

A380755 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2 / (1 - x * A(x)^2)^2) / (1 - x * A(x)^2).

Original entry on oeis.org

1, 2, 25, 622, 23601, 1211306, 78585241, 6171434550, 569338685089, 60362321078674, 7232765564919321, 966640735654507838, 142570635491126076625, 23003561321179411452858, 4030628821337323603113241, 762175215630679850520288646, 154707566043362563540600474689
Offset: 0

Views

Author

Seiichi Manyama, Feb 01 2025

Keywords

Crossrefs

Programs

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

Formula

a(n) = n! * Sum_{k=0..n} (2*n+1)^(k-1) * binomial(3*n+k,n-k)/k!.
Showing 1-5 of 5 results.