A241871 - OEIS

%I #14 Mar 07 2022 13:21:36

%S 1,0,0,1,26,937,45747,2945144,242899690,25034354941,3157647587689,

%T 478931493603308,86057396214591300,18086772915953351382,

%U 4397414569504319733812,1224945090342466220614714,387654163770235904289085798,138333762956844287480268151988

%N Number of ascent sequences of length 2n with exactly n descents.

%H Joerg Arndt and Alois P. Heinz, <a href="/A241871/b241871.txt">Table of n, a(n) for n = 0..70</a>

%F a(n) = A238858(2n,n).

%p b:= proc(n, i, t) option remember; `if`(n=0, 1, expand(add(

%p       `if`(j<i, x, 1) *b(n-1, j, t+`if`(j>i, 1, 0)), j=0..t+1)))

%p     end:

%p a:= n-> coeff(b(2*n, -1$2), x, n):

%p seq(a(n), n=0..20);

%t b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, Expand[Sum[If[j<i, x, 1]*b[n-1, j, t + If[j>i, 1, 0]], {j, 0, t+1}]]]; a[n_] := Coefficient[b[2*n, -1, -1], x, n]; Table[ a[n], {n, 0, 20}] (* _Jean-François Alcover_, Feb 13 2015, after Maple *)

%Y Cf. A238858.

%K nonn

%O 0,5

%A _Joerg Arndt_ and _Alois P. Heinz_, May 01 2014