OFFSET
0,2
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: (1+x)*(1+27*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 07 2012
E.g.f.: (x*(x+1)*29+2)*e^x-1. - Gopinath A. R., Feb 14 2012
Sum_{n>=0} 1/a(n) = 3/4 +sqrt(58)/116*Pi*coth(Pi*sqrt(58)/29) = 1.0543041946866.. - R. J. Mathar, May 07 2024
MATHEMATICA
Join[{1}, 29 Range[40]^2 + 2] (* Bruno Berselli, Feb 07 2012 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {31, 118, 263}, 50]] (* Vincenzo Librandi, Aug 03 2015 *)
PROG
(PARI) a(n)=polcoeff((x*(x+1)*29+2)*exp(x+O(x^(n+1)))-1, n)*n! /* to illustrate the e.g.f. */
(PARI) A010019(n)=29*n^2+2-!n \\ M. F. Hasler, Feb 14 2012
(Magma) [1] cat [29*n^2+2: n in [1..50]]; // Vincenzo Librandi, Aug 03 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved