OFFSET
1,1
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
a(n) = T(n,5); T(n,k) = Sum_{i=1..n} binomial(n+1,i)*binomial(k-1,i-1)*binomial(n-i+k,k).
G.f.: 2*x*(1+4*x+16*x^2+24*x^3+36*x^4+24*x^5+16*x^6+4*x^7+x^8)/(1-x)^11. - Colin Barker, Mar 17 2012
From G. C. Greubel, Jan 23 2022: (Start)
a(n) = n*(n+1)*(n^8 +4*n^7 +66*n^6 +184*n^5 +1089*n^4 +1876*n^3 +4604*n^2 +3696*n +2880)/14400.
E.g.f.: (x/14400)*(28800 +187200*x +403200*x^2 +398400*x^3 +207840*x^4 +61200*x^5 +10400*x^6 +1000*x^7 +50*x^8 +x^9)*exp(x). (End)
MATHEMATICA
Table[n*(n+1)*(n^8 +4*n^7 +66*n^6 +184*n^5 +1089*n^4 +1876*n^3 +4604*n^2 +3696*n +2880)/14400, {n, 50}] (* G. C. Greubel, Jan 23 2022 *)
PROG
(Sage) [n*(n+1)*(n^8 +4*n^7 +66*n^6 +184*n^5 +1089*n^4 +1876*n^3 +4604*n^2 +3696*n +2880)/14400 for n in (1..50)] # G. C. Greubel, Jan 23 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 22 2009
STATUS
approved