Search: id:A108044
Results 1-1 of 1 results found.

%I A108044
%S A108044 1,0,1,2,0,1,0,3,0,1,6,0,4,0,1,0,10,0,5,0,1,20,0,15,0,6,0,1,0,35,0,21,
               0,
%T A108044 7,0,1,70,0,56,0,28,0,8,0,1,0,126,0,84,0,36,0,9,0,1,252,0,210,0,120,0,
%U A108044 45,0,10,0,1,0,462,0,330,0,165,0,55,0,11,0,1,924,0,792,0,495,0,220,0,66
%N A108044 Triangle read by rows: right half of Pascal's triangle (A007318) interspersed 
               with 0's.
%D A108044 L. W. Shapiro, S. Getu, W.-J. Woan and L. C. Woodson, The Riordan group, 
               Discrete Applied Math., 34 (1991), 229-239.
%F A108044 Each entry is the sum of those in the previous row that are to its left 
               and to its right.
%F A108044 Riordan array (1/sqrt(1-4*x^2), (1-sqrt(1-4*x^2))/(2*x)).
%F A108044 T(n, k)=binomial(n, (n+k)/2) if n+k is even, T(n, k)=0 if n+k is odd. 
               G.f.=f/(1-tg), where f=1/sqrt(1-4x^2) and g=(1-sqrt(1-4x^2))/(2x). 
               - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 05 2005
%e A108044 Triangle begins:
%e A108044 .1
%e A108044 .0 1
%e A108044 .2 0 1
%e A108044 .0 3 0 1
%e A108044 .6 0 4 0 1
%e A108044 .0 10 0 5 0 1
%e A108044 .20 0 15 0 6 0 1
%p A108044 T:=proc(n,k) if n+k mod 2 = 0 then binomial(n,(n+k)/2) else 0 fi end: 
               for n from 0 to 13 do seq(T(n,k),k=0..n) od; # yields sequence in 
               triangular form (Deutsch)
%Y A108044 Cf. A007318, A108045.
%Y A108044 Sequence in context: A134511 A112554 A120616 this_sequence A104477 A052173 
               A124305
%Y A108044 Adjacent sequences: A108041 A108042 A108043 this_sequence A108045 A108046 
               A108047
%K A108044 nonn,tabl,easy
%O A108044 0,4
%A A108044 N. J. A. Sloane (njas(AT)research.att.com), Jun 02 2005
%E A108044 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and Christian 
               G. Bower (bowerc(AT)usa.net), Jun 05 2005

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