Search: id:A088855
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%I A088855
%S A088855 1,1,1,1,1,1,1,2,2,1,1,2,4,2,1,1,3,6,6,3,1,1,3,9,9,9,3,1,1,4,12,18,18,
%T A088855 12,4,1,1,4,16,24,36,24,16,4,1,1,5,20,40,60,60,40,20,5,1,1,5,25,50,100,
%U A088855 100,100,50,25,5,1,1,6,30,75,150,200,200,150,75,30,6,1,1,6,36,90,225
%N A088855 Number of symmetric Dyck paths of semilength n with k peaks.
%C A088855 Rows 2,4,6,... give A088459.
%C A088855 Diagonal sums are in A088518 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Jan 04 2009]
%C A088855 Row sums are in A001405 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Jan 04 2009]
%C A088855 Subtriangle (1<=k<=n) of triangle T(n,k), 0<=k<=n, read by rows, given 
               by A101455 DELTA A056594 := [0,1,0,-1,0,1,0,-1,0,1,0,-1,0,...] DELTA 
               [1,0,-1,0,1,0,-1,0,1,0,-1,0,1,...] where DELTA is the operator defined 
               in A084938 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 
               03 2009]
%D A088855 Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal 
               Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.
%F A088855 a(n, k)=binomial(floor(n'), floor(k'))*binomial(ceil(n'), ceil(k')), 
               where n'=(n-1)/2, k'=(k-1)/2. G.f.=2u/[uv+sqrt(xyuv)]-1, where x=1+z+tz, 
               y=1+z-tz, u=1-z+tz, v=1-z-tz.
%F A088855 Triangle T(n,k), 0<=k<=n, given by A101455 DELTA A056594 begins : 1 ; 
               0,1 ; 0,1,1 ; 0,1,1,1 ; 0,1,2,2,1 ; 0,1,2,4,2,1 ; 0,1,3,6,6,3,1 ; 
               0,1,3,9,9,9,3,1 ; ... [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Jan 03 2009]
%e A088855 Triangle begins:
%e A088855 1;
%e A088855 1,1;
%e A088855 1,1,1;
%e A088855 1,2,2,1;
%e A088855 1,2,4,2,1;
%e A088855 1,3,6,6,3,1;
%e A088855 1,3,9,9,9,3,1;
%e A088855 1,4,12,18,18,12,4,1;
%e A088855 1,4,16,24,36,24,16,4,1;
%e A088855 1,5,20,40,60,60,40,20,5,1;
%e A088855 1,5,25,50,100,100,100,50,25,5,1;
%e A088855 1,6,30,75,150,200,200,150,75,30,6,1;
%e A088855 1,6,36,90,225,300,400,300,225,90,36,6,1;
%e A088855 1,7,42,126,315,525,700,700,525,315,126,42,7,1;
%e A088855 1,7,49,147,441,735,1225,1225,1225,735,441,147,49,7,1;
%e A088855 1,8,56,196,588,1176,1960,2450,2450,1960,1176,588,196,56,8,1.
%e A088855 a(6,2)=3 because we have UUUDDDUUUDDD, UUUUDDUUDDDD, UUUUUDUDDDDD, where
%e A088855 U=(1,1), D=(1,-1).
%Y A088855 Cf. A088459.
%Y A088855 Column 2 is A008619, column 3 is A002620, column 4 is A028724, column 
               5 is A028723 and column 6 is A028725.
%Y A088855 Sequence in context: A120423 A113137 A075402 this_sequence A034851 A122085 
               A066287
%Y A088855 Adjacent sequences: A088852 A088853 A088854 this_sequence A088856 A088857 
               A088858
%K A088855 nonn
%O A088855 1,8
%A A088855 Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 24 2003

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