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.

A367837 Expansion of e.g.f. 1/(2 - x - exp(4*x)).

Original entry on oeis.org

1, 5, 66, 1294, 33752, 1100504, 43060176, 1965653232, 102548623744, 6018735869824, 392498702352128, 28155539333730560, 2203322337542003712, 186790304541786160128, 17053569926181643921408, 1668166923908523824576512, 174057374767036007615922176
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, 4^j*binomial(i, j)*v[i-j+1])); v;

Formula

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

A367838 Expansion of e.g.f. 1/(2 + x - exp(2*x)).

Original entry on oeis.org

1, 1, 6, 38, 344, 3832, 51408, 803952, 14371456, 289005440, 6457624832, 158719896832, 4255775425536, 123619815742464, 3867071262472192, 129610289219999744, 4633674344869756928, 176011269522607144960, 7079115958438736363520
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^j*binomial(i, j)*v[i-j+1])); v;

Formula

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

A367839 Expansion of e.g.f. 1/(2 + x - exp(3*x)).

Original entry on oeis.org

1, 2, 17, 183, 2679, 48903, 1071621, 27394965, 800378019, 26307021483, 960739737777, 38595129840369, 1691405818822719, 80301792637126791, 4105701241574252445, 224912022483008478141, 13142159127790633537947, 815924005186398537216483
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^j*binomial(i, j)*v[i-j+1])); v;

Formula

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