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.

A367754 E.g.f. satisfies A(x) = exp(x * (1 + x) * A(x^2/2)).

Original entry on oeis.org

1, 1, 3, 10, 49, 276, 1921, 14533, 127905, 1214524, 12923641, 146976501, 1828895113, 24160939960, 343798990809, 5162735472196, 82578544952641, 1387325644153368, 24621686929968625, 457066782857330929, 8906813110169504841, 180902690843146001416
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]/(2^(j\2)*(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) / (2^floor(k/2) * floor(k/2)! * (n-1-k)!).

A367756 E.g.f. satisfies A(x) = exp(x * (1 + x + x^2 + x^3) * A(x^4/24)).

Original entry on oeis.org

1, 1, 3, 13, 73, 386, 2671, 20728, 175393, 1553968, 15520861, 165541806, 1869485773, 22249874518, 284029764383, 3804116563276, 53328350650081, 782331158754088, 12051288543702313, 193028133988081918, 3212490296905001781, 55543932173668760221
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]/(24^(j\4)*(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) / (24^floor(k/4) * floor(k/4)! * (n-1-k)!).

A367757 E.g.f. satisfies A(x) = exp(x * (1 + x + x^2 + x^3 + x^4) * A(x^5/120)).

Original entry on oeis.org

1, 1, 3, 13, 73, 501, 3337, 27637, 254409, 2557369, 27603631, 313768731, 3905502745, 51573777841, 718307494269, 10507900625251, 161239887204721, 2608009648536417, 43989477103304155, 772109936171046001, 14085074476090366761, 266890182641557777093
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]/(120^(j\5)*(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) / (120^floor(k/5) * floor(k/5)! * (n-1-k)!).
Showing 1-3 of 3 results.