This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A099928 #17 Nov 17 2022 08:14:01
%S A099928 1,2,4,12,56,408,4608,80784,2201536,93224736,6134017792,627029574336,
%T A099928 99602689462784,24580813373119872,9426621978735869952,
%U A099928 5616371724370667073792,5199854362208758062125056,7479400854548558531507839488,16717751433807850998823619411968
%N A099928 Row sums of Pellonomial triangle A099927.
%H A099928 Alois P. Heinz, <a href="/A099928/b099928.txt">Table of n, a(n) for n = 0..70</a>
%H A099928 S. Falcon, <a href="https://www.saspublishers.com/article/2554/">On The Generating Functions of the Powers of the K-Fibonacci Numbers</a>, Scholars Journal of Engineering and Technology (SJET), 2014; 2 (4C):669-675.
%p A099928 p:= proc(n) p(n):= `if`(n<2, n, 2*p(n-1)+p(n-2)) end:
%p A099928 f:= proc(n) f(n):= `if`(n=0, 1, p(n)*f(n-1)) end:
%p A099928 a:= n-> add(f(n)/(f(k)*f(n-k)), k=0..n):
%p A099928 seq(a(n), n=0..20); # _Alois P. Heinz_, Aug 15 2013
%t A099928 p[n_] := p[n] = If[n < 2, n, 2*p[n - 1] + p[n - 2]];
%t A099928 f[n_] := f[n] = If[n == 0, 1, p[n]*f[n - 1]];
%t A099928 T[n_, k_] := f[n]/(f[k]*f[n - k]);
%t A099928 a[n_] := Sum[T[n, k], {k, 0, n}];
%t A099928 Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Nov 16 2022, after _Alois P. Heinz_ *)
%K A099928 nonn
%O A099928 0,2
%A A099928 _Ralf Stephan_, Nov 03 2004