OFFSET
0,3
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Wikipedia, Young tableau
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
a(n) = n*(180+(637+(385+58*n^2)*n^2)*n^2)/1260.
G.f.: x*(x+1)^2*(x^4+10*x^3+36*x^2+10*x+1)/(x-1)^8.
MAPLE
a:= n-> n*(180+(637+(385+58*n^2)*n^2)*n^2)/1260:
seq(a(n), n=0..40);
MATHEMATICA
CoefficientList[Series[x (x+1)^2(x^4+10x^3+36x^2+10x+1)/(x-1)^8, {x, 0, 40}], x] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 1, 20, 189, 1100, 4615, 15372, 43219}, 40] (* Harvey P. Dale, Jan 29 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Mar 21 2012
STATUS
approved