%I A097591
%S A097591 1,0,1,1,0,1,0,5,0,1,6,0,17,0,1,0,70,0,49,0,1,90,0,500,0,129,0,1,0,1890,
%T A097591 0,2828,0,321,0,1,2520,0,23100,0,13930,0,769,0,1,0,83160,0,215292,0,
%U A097591 62634,0,1793,0,1,113400,0,1549800,0,1697430,0,264072,0,4097,0,1,0
%N A097591 Triangle read by rows: T(n,k) is the number of permutations of [n] with 
               k increasing runs of odd length.
%F A097591 E.g.f.=t^2/[1-tx-(1-t^2)exp(-tx)].
%e A097591 Triangle starts:
%e A097591 1;
%e A097591 0,1;
%e A097591 1,0,1;
%e A097591 0,5,0,1;
%e A097591 6,0,17,0,1;
%e A097591 0,70,0,49,0,1;
%e A097591 Row n has n+1 entries.
%e A097591 Example: T(3,1)=5 because we have (123),13(2),(2)13,23(1) and (3)12 (the 
               runs of odd length are shown between parentheses).
%p A097591 G:=t^2/(1-t*x-(1-t^2)*exp(-t*x)): Gser:=simplify(series(G,x=0,12)): P[0]:=1: 
               for n from 1 to 11 do P[n]:=sort(expand(n!*coeff(Gser,x^n))) od: 
               seq(seq(coeff(t*P[n],t^k),k=1..n+1),n=0..11);
%Y A097591 Sequence in context: A021670 A060081 A083861 this_sequence A164652 A127557 
               A060524
%Y A097591 Adjacent sequences: A097588 A097589 A097590 this_sequence A097592 A097593 
               A097594
%K A097591 nonn,tabl
%O A097591 0,8
%A A097591 Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 29 2004