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Number weak ascent sequences of length 2n (prefixed with a zero) with exactly n weak ascents.
2

%I #12 May 25 2024 16:17:23

%S 1,0,0,1,35,1661,107002,9047970,972937247,129603346139,20934881571217,

%T 4029204458109445,910549073414709876,238643240329544375336,

%U 71772700696174395158056,24544642886642172762170933,9468192975202745545226891834,4090995487728206638560153282674

%N Number weak ascent sequences of length 2n (prefixed with a zero) with exactly n weak ascents.

%H Alois P. Heinz, <a href="/A373115/b373115.txt">Table of n, a(n) for n = 0..70</a>

%H Beata Benyi, Anders Claesson, and Mark Dukes, <a href="https://arxiv.org/abs/2111.03159">Weak ascent sequences and related combinatorial structures</a>, arXiv:2111.03159 [math.CO], 2021-2022.

%F a(n) = A369321(2n,n).

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

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

%p end:

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

%p seq(a(n), n=0..17);

%Y Cf. A357141, A369321.

%K nonn

%O 0,5

%A _Alois P. Heinz_, May 25 2024