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

0,2

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.

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 *)

Crossrefs

Sequence in context: A227037 A158569 A020106 * A363005 A000568 A177921

Adjacent sequences: A099925 A099926 A099927 * A099929 A099930 A099931

Keyword

nonn

Author

Ralf Stephan, Nov 03 2004

Status

approved