A185649 - OEIS

A185649

Expansion of g.f. 1/ (1-x^1*(1-x^(m+1))/ (1-x^2*(1-x^(m+2))/ (1- ... ))) for m=10.

%I #16 Jan 02 2023 12:30:48

%S 1,1,1,2,3,5,9,15,26,45,78,135,233,404,700,1213,2103,3645,6319,10955,

%T 18992,32927,57085,98970,171588,297489,515771,894217,1550350,2687923,

%U 4660196,8079634,14008102,24286615,42107043,73003306,126569874,219441205,380457391

%N Expansion of g.f. 1/ (1-x^1*(1-x^(m+1))/ (1-x^2*(1-x^(m+2))/ (1- ... ))) for m=10.

%H Alois P. Heinz, <a href="/A185649/b185649.txt">Table of n, a(n) for n = 0..750</a>

%H Paul D. Hanna et al., <a href="http://list.seqfan.eu/oldermail/seqfan/2013-July/011445.html">Formula Needed for a Family of Continued Fractions</a> and follow-up messages on the SeqFan list, Jul 28 2013

%t nMax = 39; col[m_ /; 0 <= m <= nMax] := 1/(1 + ContinuedFractionK[-x^k (1 - x^(m + k)), 1, {k, 1, Ceiling[nMax/2]}]) + O[x]^(2 nMax) // CoefficientList[#, x]&; A185649 = col[10][[1 ;; nMax]] (* _Jean-François Alcover_, Nov 03 2016 *)

%Y Column m=10 of A185646.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Aug 29 2013