OFFSET
1,3
LINKS
Bruno Berselli, Table of n, a(n) for n = 1..1000
X. Acloque, Polynexus Numbers and other mathematical wonders [broken link]
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = ((n^9-(n-1)^9)-(n^3-(n-1)^3))/504 = ((n^9-(n-1)^9)-(n^3-(n-1)^3))/(2^9-2^3).
a(1)=1, a(2)=38, a(3)=481, a(4)=3355, a(5)=16120, a(6)=60071, a(7)=186238, a(8)=502386, a(9)=1215435, a(n)=9*a(n-1)-36*a(n-2)+ 84*a(n-3)- 126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Jan 18 2012
G.f.: x^2*(1+29*x+175*x^2+310*x^3+175*x^4+29*x^5+x^6)/(1-x)^9. - Bruno Berselli, Feb 10 2012
MATHEMATICA
Table[((n^9-(n-1)^9)-(n^3-(n-1)^3))/504, {n, 30}] (* or *) LinearRecurrence[ {9, -36, 84, -126, 126, -84, 36, -9, 1}, {0, 1, 38, 481, 3355, 16120, 60071, 186238, 502386}, 30] (* Harvey P. Dale, Jan 18 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Xavier Acloque, Oct 21 2003
EXTENSIONS
Offset changed and first term added (according to the formula) from Bruno Berselli, Feb 08 2012
STATUS
approved