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 A134527 G.f. A(x) satisfies: A(x) = Sum_{n>=0} [x*A(x)]^(2^n-1). 1
 1, 1, 1, 2, 5, 11, 24, 58, 149, 385, 1001, 2652, 7140, 19384, 52944, 145590, 402949, 1121117, 3133255, 8793372, 24774557, 70045871, 198672464, 565144064, 1611946284, 4609140916, 13209415116, 37937455636, 109171460104, 314736939884, 908930799572, 2629120466966 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Number of Dyck n-paths with all ascent lengths being 1 less than a power of 2. [David Scambler, May 07 2012] LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: A(x) = Series_Reversion{x/[Sum_{n>=0} x^(2^n-1)]}. MAPLE b:= proc(x, y, t) option remember; `if`(x<0 or y>x, 0, `if`(x=0, 1, b(x-1, y+1, true)+`if`(t, add( b(x-2^j+1, y-2^j+1, false), j=1..ilog2(y+1)), 0))) end: a:= n-> b(2*n, 0, true): seq(a(n), n=0..32); # Alois P. Heinz, Apr 01 2019 MATHEMATICA 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 *) PROG (PARI) a(n)=polcoeff(serreverse(x/sum(j=0, #binary(n), x^(2^j-1)+ x*O(x^n))), n) CROSSREFS Cf. A075864. Sequence in context: A071879 A374565 A228862 * A124379 A302830 A084978 Adjacent sequences: A134524 A134525 A134526 * A134528 A134529 A134530 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 19 2007 STATUS approved

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Last modified September 9 16:40 EDT 2024. Contains 375765 sequences. (Running on oeis4.)