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A134527 G.f. A(x) satisfies: A(x) = Sum_{n>=0} [x*A(x)]^(2^n-1). 1

%I #16 Apr 01 2019 09:28:44

%S 1,1,1,2,5,11,24,58,149,385,1001,2652,7140,19384,52944,145590,402949,

%T 1121117,3133255,8793372,24774557,70045871,198672464,565144064,

%U 1611946284,4609140916,13209415116,37937455636,109171460104,314736939884,908930799572,2629120466966

%N G.f. A(x) satisfies: A(x) = Sum_{n>=0} [x*A(x)]^(2^n-1).

%C Number of Dyck n-paths with all ascent lengths being 1 less than a power of 2. [_David Scambler_, May 07 2012]

%H Alois P. Heinz, <a href="/A134527/b134527.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: A(x) = Series_Reversion{x/[Sum_{n>=0} x^(2^n-1)]}.

%p b:= proc(x, y, t) option remember; `if`(x<0 or y>x, 0,

%p `if`(x=0, 1, b(x-1, y+1, true)+`if`(t, add(

%p b(x-2^j+1, y-2^j+1, false), j=1..ilog2(y+1)), 0)))

%p end:

%p a:= n-> b(2*n, 0, true):

%p seq(a(n), n=0..32); # _Alois P. Heinz_, Apr 01 2019

%t f[x_, y_, d_] := f[x, y, d] = If[x < 0 || y < x, 0, If[x == 0 && y == 0, 1, f[x - 1, y, 0] + f[x, y - If[d == 0, 1, 2*d], If[d == 0, 1, 2*d]]]];Table[f[n, n, 0], {n, 0, 28}] (* _David Scambler_, May 07 2012 *)

%o (PARI) a(n)=polcoeff(serreverse(x/sum(j=0,#binary(n),x^(2^j-1)+ x*O(x^n))),n)

%Y Cf. A075864.

%K nonn

%O 0,4

%A _Paul D. Hanna_, Nov 19 2007

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)