%I A010027
%S A010027 1,1,1,1,2,3,1,3,9,11,1,4,18,44,53,1,5,30,110,265,309,1,6,45,220,795,
%T A010027 1854,2119,1,7,63,385,1855,6489,14833,16687,1,8,84,616,3710,17304,59332,
%U A010027 133496,148329,1,9,108,924,6678,38934,177996,600732,1334961,1468457,1
%N A010027 Triangle of permutations of 1..n by number of consecutive ascending pairs.
%C A010027 When seen as coefficients of polynomials with decreasing exponents: evaluations 
               are A001339 (x=2), A081923 (x=3), A081924 (x=4), A087981 (x=-1).
%C A010027 It appears that when x=1, P(n,x)=(n+1)! [From Timothy Hopper (timothyhopper(AT)hotmail.co.uk), 
               Aug 20 2009]
%D A010027 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied 
               Tables, Cambridge, 1966, p. 263.
%F A010027 E.g.f.: exp(x*(y-1))/(1-x)^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Jan 03 2003
%e A010027 P(0,x) = 1
%e A010027 P(1,x) = x + 1
%e A010027 P(2,x) = x^2 + 2x + 3
%e A010027 P(3,x) = x^3 + 3x^2 + 9x + 11
%e A010027 P(5,x) = x^4 + 4x^3 + 18x^2 + 44x + 53
%Y A010027 Cf. A000255, A000166, A000274, A000313, A001260, A001261.
%Y A010027 Sequence in context: A134319 A135091 A111589 this_sequence A151880 A108990 
               A145080
%Y A010027 Adjacent sequences: A010024 A010025 A010026 this_sequence A010028 A010029 
               A010030
%K A010027 tabl,nonn
%O A010027 1,5
%A A010027 N. J. A. Sloane (njas(AT)research.att.com).
%E A010027 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 03 2003