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A360229 Row sums of triangle A360173.

%I A360229 #16 Apr 24 2025 06:49:40
%S A360229 0,1,3,6,16,36,73,156,324,677,1405,2864,5906,12058,24548,49928,101434,
%T A360229 206173,417141,844256,1707622,3452998,6970196,14058528,28368774,
%U A360229 57197983,115239846,232020596,467296470,940684267,1892396396,3805806218,7654402454,15391563411
%N A360229 Row sums of triangle A360173.
%H A360229 Alois P. Heinz, <a href="/A360229/b360229.txt">Table of n, a(n) for n = 0..800</a>
%p A360229 b:= proc(n) option remember; `if`(n=0, 1, (p->
%p A360229        add((t-> `if`(i<n, 0, t*x^(i-n))+t*x^(i+n))(
%p A360229       coeff(p, x, i)), i=0..degree(p)))(b(n-1)))
%p A360229     end:
%p A360229 a:= proc(n) option remember; (p->
%p A360229       add(i*coeff(p, x, i), i=0..degree(p)))(b(n))
%p A360229     end:
%p A360229 seq(a(n), n=0..35);  # _Alois P. Heinz_, Jan 30 2023
%t A360229 b[n_] := b[n] = If[n == 0, 1, Function[p, Sum[Function[t, If[i<n, 0, t*x^(i-n)]+t*x^(i+n)][Coefficient[p, x, i]], {i, 0, Exponent[p, x]}]][b[n-1]]];
%t A360229 a[n_] := a[n] = Function[p, Sum[i*Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][b[n]];
%t A360229 Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Apr 24 2025, after _Alois P. Heinz_ *)
%Y A360229 Cf. A141001, A141002, A360173.
%K A360229 nonn
%O A360229 0,3
%A A360229 _John Tyler Rascoe_, Jan 30 2023