A099928 Row sums of Pellonomial triangle A099927.

1, 2, 4, 12, 56, 408, 4608, 80784, 2201536, 93224736, 6134017792, 627029574336, 99602689462784, 24580813373119872, 9426621978735869952, 5616371724370667073792, 5199854362208758062125056, 7479400854548558531507839488, 16717751433807850998823619411968

Offset: 0

Author

Ralf Stephan, Nov 03 2004

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..70
• S. Falcon, On The Generating Functions of the Powers of the K-Fibonacci Numbers, Scholars Journal of Engineering and Technology (SJET), 2014; 2 (4C):669-675.

Programs

Maple

p:= proc(n) p(n):= `if`(n<2, n, 2*p(n-1)+p(n-2)) end:
f:= proc(n) f(n):= `if`(n=0, 1, p(n)*f(n-1)) end:
a:= n-> add(f(n)/(f(k)*f(n-k)), k=0..n):
seq(a(n), n=0..20);  # Alois P. Heinz, Aug 15 2013

Mathematica

p[n_] := p[n] = If[n < 2, n, 2*p[n - 1] + p[n - 2]];
f[n_] := f[n] = If[n == 0, 1, p[n]*f[n - 1]];
T[n_, k_] := f[n]/(f[k]*f[n - k]);
a[n_] := Sum[T[n, k], {k, 0, n}];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Nov 16 2022, after Alois P. Heinz *)