# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a210737 Showing 1-1 of 1 %I A210737 #17 Apr 28 2018 18:17:05 %S A210737 1,0,1,1,2,6,8,29,50,141,327,771,2047,4746,12644,30941,79886,204885, %T A210737 522242,1365056,3505825,9185742,23907116,62636476,164624803,432540010, %U A210737 1142827935,3017208675,7996379870,21211540268,56369770281,150086840133,400009010758 %N A210737 Number of Dyck n-paths all of whose ascents have prime lengths. %H A210737 Alois P. Heinz, Table of n, a(n) for n = 0..700 %F A210737 a(n) ~ c * d^n / n^(3/2), where d = 2.7925684676903082567..., c = 0.4016264581712556... . - _Vaclav Kotesovec_, Sep 02 2014 %e A210737 a(0) = 1: the empty path. %e A210737 a(1) = 0. %e A210737 a(2) = 1: UUDD. %e A210737 a(3) = 1: UUUDDD. %e A210737 a(4) = 2: UUDDUUDD, UUDUUDDD. %e A210737 a(5) = 6: UUDDUUUDDD, UUDUUUDDDD, UUUDDDUUDD, UUUDDUUDDD, UUUDUUDDDD, UUUUUDDDDD. %e A210737 a(6) = 8: UUDDUUDDUUDD, UUDDUUDUUDDD, UUDUUDDDUUDD, UUDUUDDUUDDD, UUDUUDUUDDDD, UUUDDDUUUDDD, UUUDDUUUDDDD, UUUDUUUDDDDD. %p A210737 with(numtheory): %p A210737 b:= proc(x, y, u) option remember; %p A210737 `if`(x<0 or y b(n, n, true): %p A210737 seq(a(n), n=0..40); %t A210737 b[x_, y_, u_] := b[x, y, u] = If[x<0 || y