Search: id:A097805
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%I A097805
%S A097805 1,0,1,0,1,1,0,1,2,1,0,1,3,3,1,0,1,4,6,4,1,0,1,5,10,10,5,1,0,1,6,15,20,
%T A097805 15,6,1,0,1,7,21,35,35,21,7,1,0,1,8,28,56,70,56,28,8,1,0,1,9,36,84,126,
%U A097805 126,84,36,9,1,0,1,10,45,120,210,252,210,120,45,10,1,0,1,11,55,165,330,
               462
%N A097805 Riordan array (1,1/(1-x)) read by rows.
%C A097805 Columns have g.f. (x/(1-x))^k. Reverse of A071919. Row sums are A011782. 
               Diagonal sums are Fib(n-1). Inverse as Riordan array is (1,1/(1+x)). 
               A097805=B*A059260*B^(-1), where B is the binomial matrix.
%C A097805 (0,1)-Pascal triangle . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 21 2006
%C A097805 (n+1) * each term of row n generates triangle A127952: (1; 0, 2; 0, 3, 
               3; 0, 4, 8, 4;...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 
               09 2007
%C A097805 Triangle T(n,k), 0<=k<=n, read by rows, given by [0,1,0,0,0,0,0,...] 
               DELTA [1,0,0,0,0,0,0,...] where DELTA is the operator defined in 
               A084938 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 12 
               2008]
%F A097805 Number triangle T(n, k) defined by T(n, k)=sum{j=0..n, binomial(n, j)*if(k<=j, 
               (-1)^(j-k), 0)}
%F A097805 G.f.: 1 +x(x +x^3(1+x) +x^6(1+x)^2 +x^10(1+x)^3 +...) . - Michael Somos 
               Aug 20 2006
%e A097805 Rows begin {1}, {0,1}, {0,1,1}, {0,1,2,1}, ....
%o A097805 (PARI) {a(n)=local(m); if(n<2, n==0, n--; m=(sqrtint(8*n+1)-1)\2; binomial(m-1,
               n-m*(m+1)/2))} /* Michael Somos Aug 20 2006 */
%Y A097805 Cf. A127952.
%Y A097805 Sequence in context: A119337 A110555 A071919 this_sequence A167763 A127839 
               A017827
%Y A097805 Adjacent sequences: A097802 A097803 A097804 this_sequence A097806 A097807 
               A097808
%K A097805 easy,nonn,tabl
%O A097805 0,9
%A A097805 Paul Barry (pbarry(AT)wit.ie), Aug 25 2004
%E A097805 Corrected by Philippe DELEHAM, Oct 05 2005

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