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.

A367835 Expansion of e.g.f. 1/(2 - x - exp(2*x)).

Original entry on oeis.org

1, 3, 22, 242, 3544, 64872, 1424976, 36517840, 1069533824, 35240047232, 1290137297152, 51955085596416, 2282489348834304, 108630445541684224, 5567741266098944000, 305752314499878569984, 17909736027185859100672, 1114647522476340562132992
Offset: 0

Views

Author

Seiichi Manyama, Dec 02 2023

Keywords

Crossrefs

Programs

  • Maple
    A367835 := proc(n)
        option remember ;
        if n = 0 then
            1 ;
        else
            n*procname(n-1)+add(2^k*binomial(n,k)*procname(n-k),k=1..n) ;
        end if;
    end proc:
    seq(A367835(n),n=0..70) ; # R. J. Mathar, Dec 04 2023
  • 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).

A367840 Expansion of e.g.f. 1/(2 + x - exp(4*x)).

Original entry on oeis.org

1, 3, 34, 514, 10456, 265704, 8103120, 288302480, 11722944896, 536262671488, 27256865214208, 1523936708699904, 92949383868668928, 6141694449341637632, 437033351625771001856, 33319937543640487708672, 2709708041047388536274944
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).

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.