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.

A385979 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * binomial(k+2,2) * binomial(n-1,k) * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 7, 145, 6449, 522096, 69506737, 14186121706, 4212887224905, 1747635451186240, 979909591959562571, 722787600597422326704, 685585597413868516073953, 820283211774547803576454720, 1217648676024408903145299884925, 2210504358495882876855897821031376
Offset: 0

Views

Author

Seiichi Manyama, Jul 14 2025

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (j+1)*binomial(j+2, 2)*binomial(i-1, j)*v[j+1]*v[i-j])); v;

Formula

E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..2} binomial(2,k) * x^(k+1)/k! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.

A385981 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * binomial(k+4,4) * binomial(n-1,k) * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 11, 526, 75981, 27017601, 20599793857, 30432196412318, 80590529100023889, 359767027014797719000, 2575966649397129017224661, 28392489655027195386265889544, 465411261102140455922541427819489, 11017701081052339904298545720453122836, 367264434033142995461894471693185212854475
Offset: 0

Views

Author

Seiichi Manyama, Jul 14 2025

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (j+1)*binomial(j+4, 4)*binomial(i-1, j)*v[j+1]*v[i-j])); v;

Formula

E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..4} binomial(4,k) * x^(k+1)/k! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.

A385982 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * binomial(k+5,5) * binomial(n-1,k) * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 13, 856, 195525, 124248221, 188647130983, 611439299390984, 3879035706651051809, 44966039381652540837592, 900671755790709615794856671, 29761825253146859538914816137428, 1560353636451919718380582807368070417, 125541398272463750591414559674298911706684
Offset: 0

Views

Author

Seiichi Manyama, Jul 14 2025

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (j+1)*binomial(j+5, 5)*binomial(i-1, j)*v[j+1]*v[i-j])); v;

Formula

E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..5} binomial(5,k) * x^(k+1)/k! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.
Showing 1-3 of 3 results.