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

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

Author

Paul D. Hanna, Sep 26 2003

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..100

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