OFFSET
0,2
COMMENTS
Binomial transform of [1, 6, 14, 9, 0, 0, 0,...].
Row sums of triangle A033292.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
From R. J. Mathar, Aug 29 2008: (Start)
G.f.: (1 +3*x +5*x^2)/(1-x)^4.
From G. C. Greubel, May 30 2021: (start)
a(n) = (n+1)*(3*n^2 +2*n +2)/2.
E.g.f.: (1/2)*(2 +12*x +14*x^2 +3*x^3)*exp(x). (End)
EXAMPLE
a(3) = 70 = (1, 3, 3, 1) dot (1, 6, 14, 9) = (1 + 18 + 42 + 9). a(3) = 70 = sum of row 3 terms of triangle A033292: (13 + 16 + 19, + 22).
MATHEMATICA
Table[(n+1)*(3*n^2+2*n+2)/2, {n, 0, 50}] (* G. C. Greubel, May 30 2021 *)
PROG
(Sage) [(n+1)*(3*n^2+2*n+2)/2 for n in (0..50)] # G. C. Greubel, May 30 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Aug 29 2008
EXTENSIONS
Extended beyond a(14) by R. J. Mathar, Aug 29 2008
STATUS
approved