This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A010030 #13 Jul 08 2025 01:28:27 %S A010030 1,1,0,3,0,3,8,1,25,28,7,17,155,143,45,259,1005,933,323,131,2770,7488, %T A010030 7150,2621,3177,27978,64164,62310,23811,1281,51433,294602,619986, %U A010030 607445,239653 %N A010030 Irregular triangle read by rows: T(n,k) (n >= 1, 0 <= k <= [n/2]) = number of permutations of 1..n with [n/2]-k runs of consecutive pairs up and down (divided by 2). %D A010030 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 264. %F A010030 G.f. for number of permutations of 1..n by number of runs of consecutive pairs up and down is Sum(n!*(((1-y)*(2*x^2-x^3)-x)/((1-y)*x^2-1))^n,n = 0 .. infinity), cf. A010029. - _Vladeta Jovovic_, Nov 23 2007 %e A010030 Triangle begins: %e A010030 1, %e A010030 1, 0, %e A010030 3, 0, %e A010030 3, 8, 1, %e A010030 25, 28, 7, %e A010030 17, 155, 143, 45, %e A010030 259, 1005, 933, 323, %e A010030 131, 2770, 7488, 7150, 2621, %e A010030 3177, 27978, 64164, 62310, 23811, %e A010030 1281, 51433, 294602, 619986, 607445, 239653, %e A010030 ... %Y A010030 Cf. A002464, A001266, A000239, A000544, A001282. %K A010030 tabf,nonn %O A010030 1,4 %A A010030 _N. J. A. Sloane_ %E A010030 More terms from _Vladeta Jovovic_, Nov 23 2007 %E A010030 Entry revised by _N. J. A. Sloane_, Apr 14 2014