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.

A367747 E.g.f. satisfies A(x) = exp(x * (1 + x) * A(x^2)).

Original entry on oeis.org

1, 1, 3, 13, 73, 561, 4771, 49813, 562353, 7340833, 102829411, 1627648221, 27294311353, 502042022353, 9759264753603, 205434011254501, 4544894700204001, 107346788357502273, 2657668122191037763, 69701762677026498733, 1909106308252976007081
Offset: 0

Views

Author

Seiichi Manyama, Nov 29 2023

Keywords

Crossrefs

Programs

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

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..n-1} (k+1) * a(floor(k/2)) * a(n-1-k) / (floor(k/2)! * (n-1-k)!).

A367749 E.g.f. satisfies A(x) = exp(x * (1 + x + x^2 + x^3) * A(x^4)).

Original entry on oeis.org

1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4777993, 62569891, 893927541, 13827333433, 234241234813, 4212828738483, 80727388033321, 1641227208417121, 35581993575319953, 810641581182744643, 19416795485684156893, 487647253209539939241
Offset: 0

Views

Author

Seiichi Manyama, Nov 29 2023

Keywords

Crossrefs

Programs

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

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..n-1} (k+1) * a(floor(k/4)) * a(n-1-k) / (floor(k/4)! * (n-1-k)!).

A367751 E.g.f. satisfies A(x) = exp(x * (1 + x + x^2 + x^3 + x^4) * A(x^5)).

Original entry on oeis.org

1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4596553, 58941091, 844031541, 12949163833, 213873687613, 3782022682803, 71267635330921, 1439160383457121, 30612704101371153, 686728250047551043, 16198763975779425373, 400727742254252310441
Offset: 0

Views

Author

Seiichi Manyama, Nov 29 2023

Keywords

Crossrefs

Programs

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

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..n-1} (k+1) * a(floor(k/5)) * a(n-1-k) / (floor(k/5)! * (n-1-k)!).
Showing 1-3 of 3 results.