OFFSET
0,2
COMMENTS
FORMULA
Recurrence: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2 with initial values a(0) = 1, a(1) = 101 and a(2) = 401.
From Stefano Spezia, Jan 06 2019: (Start)
O.g.f.: (-1 - 98*x - 101*x^2)/(-1 + x)^3.
E.g.f.: exp(x)*(1 + 100*x + 100*x^2).
(End)
MATHEMATICA
a[n_] := 1 + 100*n^2 ; Array[a, 50, 0] (* or *)
CoefficientList[Series[(-1 - 98 x - 101 x^2)/(-1 + x)^3, {x, 0, 50}], x] (* or *)
CoefficientList[Series[E^x (1 + 100 x + 100 x^2), {x, 0, 50}], x]*Table[n!, {n, 0, 50}] (* Stefano Spezia, Jan 06 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Curtz, Jan 06 2019
EXTENSIONS
Corrected and extended (recurrence formula) by Werner Schulte, Feb 18 2019
STATUS
approved