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 (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
FORMULA
a(n) = ((n^14-(n-1)^14)-(n^2-(n-1)^2))/16380 = ((n^14-(n-1)^14)-(n^2-(n-1)^2))/(2^14-2^2).
G.f.: x^2*(1+x)*(1+276*x+11837*x^2+145168*x^3+638914*x^4+1068728*x^5+638914*x^6+145168*x^7+11837*x^8+276*x^9+x^10)/(1-x)^14. - Bruno Berselli, Feb 08 2012
MATHEMATICA
Table[((n^14 - (n - 1)^14) - (n^2 - (n - 1)^2))/16380, {n, 20}] (* Bruno Berselli, Feb 08 2012 *)
LinearRecurrence[{14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91, 14, -1}, {0, 1, 291, 16096, 356232, 4411517, 36621423, 227095448, 1128128568, 4708376529, 17078744419, 55199550120, 161993768080, 438011626365}, 20] (* Harvey P. Dale, Mar 04 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Xavier Acloque, Oct 21 2003
EXTENSIONS
First term added according to the formula from Bruno Berselli, Feb 08 2012
STATUS
approved