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.

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A367828 E.g.f. A(x) satisfies A(x) = (1 - log(1 - x) * A(2*x)) / (1 - x).

Original entry on oeis.org

1, 2, 13, 209, 7874, 687194, 138026428, 63273019396, 65547617642192, 151904702763916944, 780028188748068778464, 8799101018162158392857376, 216405047530763040469557821568, 11527355297347542160143184818391680, 1322291382391922104463259686181056293632
Offset: 0

Views

Author

Seiichi Manyama, Dec 02 2023

Keywords

Crossrefs

Programs

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

Formula

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

A367922 Expansion of e.g.f. 1/(1 - x + 2*log(1 - x)).

Original entry on oeis.org

1, 3, 20, 202, 2724, 45928, 929288, 21936864, 591822912, 17962293408, 605744322048, 22470338716032, 909323575700352, 39864781715364864, 1882110048700328448, 95205899353680970752, 5137022051563160623104, 294501790029090740576256
Offset: 0

Views

Author

Seiichi Manyama, Dec 05 2023

Keywords

Crossrefs

Programs

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

Formula

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

A367923 Expansion of e.g.f. 1/(1 - x + 3*log(1 - x)).

Original entry on oeis.org

1, 4, 35, 462, 8136, 179112, 4731786, 145838844, 5137045848, 203566459392, 8963064065088, 434109674396736, 22936702911358608, 1312878755037640320, 80928769156102447920, 5344960170283958863008, 376543135663291116638208, 28184733661095459402610176
Offset: 0

Views

Author

Seiichi Manyama, Dec 05 2023

Keywords

Crossrefs

Programs

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

Formula

a(0) = 1; a(n) = n * a(n-1) + 3 * Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k).

A367829 E.g.f. A(x) satisfies A(x) = (1 - log(1 - x) * A(3*x)) / (1 - x).

Original entry on oeis.org

1, 2, 17, 530, 60332, 24882484, 36501847110, 186651759218364, 3267898148335418280, 193010228785740170125728, 37993098362777240856612204096, 24678625994736515097158433120107040, 52461378922253347510159057679901573120528
Offset: 0

Views

Author

Seiichi Manyama, Dec 02 2023

Keywords

Crossrefs

Programs

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

Formula

a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} 3^(n-k) * (k-1)! * binomial(n,k) * a(n-k).
Previous Showing 11-14 of 14 results.