OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
a(n) = 1 + 7*n + 27*n^2 + 75*n^3 + 165*n^4 + 297*n^5 + 429*n^6 + 429*n^7, compare to row n = 7 of Catalan triangle A009766.
G.f.: (1 + 1422*x + 83823*x^2 + 616894*x^3 + 1013799*x^4 + 412698*x^5 + 33337*x^6 + 186*x^7)/(1 - x)^8.
E.g.f.: exp(x)*(1 + 1429*x + 46188*x^2 + 176229*x^3 + 181170*x^4 + 66792*x^5 + 9438*x^6 + 429*x^7). - Stefano Spezia, Jul 24 2022
MATHEMATICA
CoefficientList[Series[(1 + 1422 x + 83823 x^2 + 616894 x^3 + 1013799 x^4 + 412698 x^5 + 33337 x^6 + 186 x^7)/(1 - x)^8, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 15 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 13 2001
STATUS
approved