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A369476 Total number of weak ascents in all length-n weak ascent sequences.

%I A369476 #11 Jan 24 2024 17:35:18
%S A369476 0,1,4,17,83,461,2873,19846,150418,1240398,11051017,105740309,
%T A369476 1081101474,11758967146,135544030566,1650178088102,21155166649234,
%U A369476 284821038726404,4017445572746953,59238368957321225,911319667593472401,14600491369553323529,243205500769215401307
%N A369476 Total number of weak ascents in all length-n weak ascent sequences.
%C A369476 See A369321 for definitions.
%H A369476 Alois P. Heinz, <a href="/A369476/b369476.txt">Table of n, a(n) for n = 0..400</a>
%F A369476 a(n) = Sum_{k=0..n} k * A369321(n,k).
%F A369476 a(n) = A336070(n+1) - A336070(n).
%p A369476 b:= proc(n, i, t) option remember; `if`(n=0, 1,
%p A369476       add(b(n-1, j, t+`if`(j>=i, 1, 0)), j=0..t+1))
%p A369476     end:
%p A369476 a:= n-> b(n+1, -1$2)-b(n, -1$2):
%p A369476 seq(a(n), n=0..23);
%Y A369476 Cf. A336070, A369321.
%K A369476 nonn
%O A369476 0,3
%A A369476 _Alois P. Heinz_, Jan 23 2024