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.

A285381 G.f.: 1/(1 - 1!*x/(1 - 2!*x^2/(1 - 3!*x^3/(1 - 4!*x^4/(1 - 5!*x^5/(1 - 6!*x^6/(1 - ...))))))), a continued fraction.

Original entry on oeis.org

1, 1, 1, 3, 5, 11, 33, 67, 169, 435, 1265, 3035, 8025, 22243, 60721, 191307, 491657, 1404371, 4089633, 12183835, 36872377, 126189219, 350136977, 1062359147, 3386475177, 10757830387, 36121721857, 120817807419, 482847966617, 1391650703939, 4654331013489
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 17 2017

Keywords

Examples

			G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 5*x^4 + 11*x^5 + 33*x^6 + 67*x^7 + 169*x^8 + ...
		

Crossrefs

Programs

  • Mathematica
    nmax = 30; CoefficientList[Series[1/(1 + ContinuedFractionK[-k! x^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x]
  • 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); \\ Seiichi Manyama, Apr 16 2021

A343428 G.f.: 1 + 1!*x/(1 + 2!*x/(1 + 3!*x/(1 + 4!*x/(1 + 5!*x/(1 + ...))))).

Original entry on oeis.org

1, 1, -2, 16, -416, 47104, -31623680, 151868796928, -5929687248674816, 2103645975156790263808, -7506342628191723555983065088, 295743482602620866090259230372134912, -140189608695401234244797733914829257462251520, 865523452956329002149153403380412177220307414830546944
Offset: 0

Views

Author

Seiichi Manyama, Apr 15 2021

Keywords

Crossrefs

Programs

  • PARI
    a(n) = my(A=1+O(x)); for(i=1, n, A=1+(n-i+1)!*x/A); polcoef(A, n);

Formula

G.f.: 1/(Sum_{k>=0} A285380(k) * (-x)^k).

A307084 Expansion of 1/(1 - 1^1*x/(1 - 2^2*x/(1 - 3^3*x/(1 - 4^4*x/(1 - 5^5*x/(1 - ...)))))), a continued fraction.

Original entry on oeis.org

1, 1, 5, 133, 31769, 95375641, 4353388262525, 3536446917781244413, 58773633134246903294470769, 22612364832863674279489837434733681, 224919094724957152626614652086970769074005045, 63900685361274641827300282511815586348785532532913331893
Offset: 0

Views

Author

Ilya Gutkovskiy, Mar 23 2019

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 11; CoefficientList[Series[1/(1 + ContinuedFractionK[-k^k x, 1, {k, 1, nmax}]), {x, 0, nmax}], x]
  • PARI
    a(n) = my(A=1+O(x)); for(i=1, n, A=1-(n-i+1)^(n-i+1)*x/A); polcoef(1/A, n); \\ Seiichi Manyama, Apr 15 2021

Formula

a(n) ~ A002109(n). - Vaclav Kotesovec, Apr 15 2021
Showing 1-3 of 3 results.