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.

A386443 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} k^2 * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 2, 11, 120, 2166, 58642, 2231959, 113926332, 7522541374, 624529876412, 63711767096254, 7837308575551868, 1144321503810951264, 195687862794184808186, 38747465910056072904383, 8795888226933223095245628, 2269380895962602685279019270, 660399219910352767447886420340
Offset: 0

Views

Author

Seiichi Manyama, Jul 22 2025

Keywords

Crossrefs

Programs

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

Formula

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

A386444 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} k^3 * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 2, 19, 550, 36314, 4612644, 1005608259, 346940795318, 178328747938574, 130358697631572620, 130619605078238043630, 174116069712361545382300, 301220935342882714418320660, 662385014999576998657776303368, 1818909557774291764795223960949603, 6142458248209027135766781428841480918
Offset: 0

Views

Author

Seiichi Manyama, Jul 22 2025

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, j^3*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x - x*Sum_{k=1..3} Stirling2(3,k) * x^k * (d^k/dx^k A(x)) ).

A386446 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} k^5 * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 2, 67, 16414, 16840826, 52661283276, 409599480216723, 6884957718009061046, 225620064835937122627934, 13323090455565480199133495252, 1332335691963961772604470940370302, 214576660211223693770379106296061734124, 53393968668333658608864584261609697870131860
Offset: 0

Views

Author

Seiichi Manyama, Jul 22 2025

Keywords

Crossrefs

Programs

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

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x - x*Sum_{k=1..5} Stirling2(5,k) * x^k * (d^k/dx^k A(x)) ).

A386447 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} k^6 * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 2, 131, 95760, 392424606, 6132419429842, 286126426174265119, 33663060172069656177612, 8824636572155130972996888814, 4689791333849576329442118802082252, 4689800713441077274969296364554337253614, 8308277421310507219950890075481144453543272228
Offset: 0

Views

Author

Seiichi Manyama, Jul 22 2025

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, j^6*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x - x*Sum_{k=1..6} Stirling2(6,k) * x^k * (d^k/dx^k A(x)) ).

A386507 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * k^4 * binomial(n-1,k) * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 3, 151, 49525, 63641021, 239036610181, 2170214958201445, 41702857906969051017, 1537709560908537888618409, 100904503302575334820438217641, 11100605398391683050596962755215561, 1950420777626865443224119613333235611309, 525796384523344023260217345195483215249534941
Offset: 0

Views

Author

Seiichi Manyama, Jul 24 2025

Keywords

Crossrefs

Programs

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

Formula

E.g.f. A(x) satisfies A(x) = exp( x + x*Sum_{k=1..4} Stirling2(4,k) * x^k * (d^k/dx^k A(x)) ).
Showing 1-5 of 5 results.