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.

A088357 G.f. = continued fraction: A(x)=1/(1-x/(1-2*x^2/(1-3*x^3/(1-4*x^4/(...))))).

Original entry on oeis.org

1, 1, 1, 3, 5, 11, 27, 55, 127, 285, 647, 1457, 3297, 7489, 16945, 38523, 87293, 198179, 449907, 1021135, 2318527, 5263581, 11950967, 27133985, 61609953, 139888777, 317629465, 721215027, 1637598485, 3718378619, 8443065363, 19171129327
Offset: 0

Views

Author

Paul D. Hanna, Sep 26 2003

Keywords

Links

Crossrefs

Cf. A005169, A285381.

Programs

  • Mathematica
    nmax = 50; CoefficientList[Series[1/Fold[(1 - #2/#1) &, 1, Reverse[Range[nmax + 1]*x^Range[nmax + 1]]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 25 2017 *)
  • PARI
    S=1; L=30; for(k=1,L,m=L-k+1; S=1/(1-m*x^m*S)+x*O(x^L)); A(x)=S; a(n)=polcoeff(A(x),n,x)

Formula

G.f.: T(0), where T(k) = 1 - x^(k+1)*(k+1)/( x^(k+1)*(k+1) - 1/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Oct 26 2013
a(n) ~ c * d^n, where d = 2.2706470084004562621321821916243432273516... and c = 0.1745837410025587240288929391139119506... - Vaclav Kotesovec, Aug 25 2017

A343420 G.f.: 1/(1 - (1*x)/(1 - (2*x)^2/(1 - (3*x)^3/(1 - (4*x)^4/(1 - (5*x)^5/(1 - ...)))))).

Original entry on oeis.org

1, 1, 1, 5, 9, 29, 173, 397, 1629, 7105, 47317, 136649, 612009, 3239657, 16725833, 144512653, 442002033, 2348928709, 13503344821, 87284090069, 570544117893, 6090993985577, 19814091021725, 112414559500753, 771831588041361, 5354065003116817, 43960328737547473
Offset: 0

Views

Author

Seiichi Manyama, Apr 16 2021

Keywords

Links

Crossrefs

Cf. A285381, A307084, A343473.

Programs

  • Mathematica
    nmax = 26;
CoefficientList[1/(1 + ContinuedFractionK[-(k x)^k, 1, {k, 1, nmax}]) + O[x]^(nmax+1), x] (* Jean-François Alcover, Apr 18 2021 *)
  • PARI
    a(n) = my(A=1+O(x)); for(i=1, n, A=1-((n-i+1)*x)^(n-i+1)/A); polcoef(1/A, n);

A343472 G.f.: 1 + 1!*x/(1 + 2!*x^2/(1 + 3!*x^3/(1 + 4!*x^4/(1 + 5!*x^5/(1 + ...))))).

Original entry on oeis.org

1, 1, 0, -2, 0, 4, 12, -8, -48, -56, -144, 400, 1200, 1792, 960, 16864, -34560, -170816, -320064, -632960, -869376, -15780224, 30636288, 144493312, 360770304, 738095104, 2382729216, 6661606912, 81815537664, -152267942912, -883849860096, -2187970242560, -6499788165120
Offset: 0

Views

Author

Seiichi Manyama, Apr 16 2021

Keywords

Crossrefs

Cf. A285381, A343428.

Programs

  • PARI
    a(n) = my(A=1+O(x)); for(i=1, n, A=1+(n-i+1)!*x^(n-i+1)/A); polcoef(A, n);
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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