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Total number of weak ascents in all length-n weak ascent sequences.
1

%I #11 Jan 24 2024 17:35:18

%S 0,1,4,17,83,461,2873,19846,150418,1240398,11051017,105740309,

%T 1081101474,11758967146,135544030566,1650178088102,21155166649234,

%U 284821038726404,4017445572746953,59238368957321225,911319667593472401,14600491369553323529,243205500769215401307

%N Total number of weak ascents in all length-n weak ascent sequences.

%C See A369321 for definitions.

%H Alois P. Heinz, <a href="/A369476/b369476.txt">Table of n, a(n) for n = 0..400</a>

%F a(n) = Sum_{k=0..n} k * A369321(n,k).

%F a(n) = A336070(n+1) - A336070(n).

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

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

%p end:

%p a:= n-> b(n+1, -1$2)-b(n, -1$2):

%p seq(a(n), n=0..23);

%Y Cf. A336070, A369321.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jan 23 2024