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.

A385835 a(n) = 1 + Sum_{k=0..n-1} (1 + k^2) * a(k) * a(n-1-k).

Original entry on oeis.org

1, 2, 7, 51, 660, 13350, 390886, 15728919, 836469748, 56989647229, 4849599126797, 504709937298467, 63117270187248665, 9344222191368190761, 1616899887657388367640, 323430766605746093449465, 74074314477265886578774322, 19261037812212680097678843345, 5643873902659784713257894768422
Offset: 0

Views

Author

Seiichi Manyama, Jul 09 2025

Keywords

Crossrefs

Programs

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

Formula

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

A385843 a(n) = 1 + Sum_{k=0..n-1} k^5 * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 2, 66, 16105, 16507753, 51603272051, 401318681776723, 6745364508844808841, 221038850400001766938953, 13052344129663319516736911260, 1305247465753403752473945799113276, 210212714880649951675343095297590137757, 52307860484508916277278208388919504757392477
Offset: 0

Views

Author

Seiichi Manyama, Jul 09 2025

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+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) * ( 1 - x*Sum_{k=1..5} Stirling2(5,k) * x^k * (d^k/dx^k A(x)) ) ).

A385836 a(n) = 1 + Sum_{k=0..n-1} (1 + k^3) * a(k) * a(n-1-k).

Original entry on oeis.org

1, 2, 7, 79, 2446, 166618, 21508712, 4732995201, 1642479584974, 847546182102241, 621260202463120771, 623749689526374747439, 832709044623310548285995, 1442255257225526024262579955, 3174408056872712362090099214740, 8723280646832436679639469748539639
Offset: 0

Views

Author

Seiichi Manyama, Jul 09 2025

Keywords

Crossrefs

Programs

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

Formula

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

A385837 a(n) = 1 + Sum_{k=0..n-1} (1 + k^4) * a(k) * a(n-1-k).

Original entry on oeis.org

1, 2, 7, 135, 11472, 2983290, 1876558882, 2439543938823, 5867113337771476, 24055177364999767957, 157922269330003687462469, 1579854504025376907525660119, 23136970006572094830720177877037, 479860765871358769352536441406761329, 13707222893156109310485886790873337444816
Offset: 0

Views

Author

Seiichi Manyama, Jul 09 2025

Keywords

Crossrefs

Programs

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

Formula

G.f. A(x) satisfies A(x) = 1/( (1 - x) * ( 1 - x*A(x) - x*Sum_{k=1..4} Stirling2(4,k) * x^k * (d^k/dx^k A(x)) ) ).

A385839 a(n) = 1 + Sum_{k=0..n-1} (1 + k^6) * a(k) * a(n-1-k).

Original entry on oeis.org

1, 2, 7, 471, 345240, 1415486250, 22122636527386, 1032242227753172079, 121446394933841583123508, 31836929544298684420302348229, 16919577022277987344334514604394117, 16919644700745370569015746375165719379327, 29974250364360598877961318618919670090162246645
Offset: 0

Views

Author

Seiichi Manyama, Jul 09 2025

Keywords

Crossrefs

Programs

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

Formula

G.f. A(x) satisfies A(x) = 1/( (1 - x) * ( 1 - x*A(x) - x*Sum_{k=1..6} Stirling2(6,k) * x^k * (d^k/dx^k A(x)) ) ).
Showing 1-5 of 5 results.