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.

A380723 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2) / (1 - x*A(x)^2).

Original entry on oeis.org

1, 2, 21, 436, 13785, 589206, 31825381, 2080523880, 159761186577, 14097898530730, 1405926737063541, 156379679761925148, 19195200442017128425, 2577494115099820986174, 375845854490491567916805, 59145488004443221188738256, 9990898494797767848442559649, 1803160967691789114062089511250
Offset: 0

Views

Author

Seiichi Manyama, Jan 30 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!.

A377889 E.g.f. A(x) satisfies A(x) = exp(x * A(x))/(1 - x*A(x)^3).

Original entry on oeis.org

1, 2, 21, 472, 16581, 795736, 48509641, 3589729760, 312603962985, 31321633489408, 3549706188092541, 448973808123051520, 62697159481460439469, 9581292408000225087488, 1590488540940006100524657, 284993765391981838318575616, 54826610288277007690469896017
Offset: 0

Views

Author

Seiichi Manyama, Nov 10 2024

Keywords

Crossrefs

Programs

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

Formula

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