A088892 Polynexus numbers of order 14.

0, 1, 291, 16096, 356232, 4411517, 36621423, 227095448, 1128128568, 4708376529, 17078744419, 55199550120, 161993768080, 438011626365, 1103841220991, 2616890599056, 5880356075792, 12602902382337, 25897027973187, 51245013077968, 98017089897528, 181801058663389

Offset: 1

Author

Xavier Acloque, Oct 21 2003

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A079547, A083200, A088889, A088890, A088891, A088893, A088894.

Programs

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 *)

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

Extensions

First term added according to the formula from Bruno Berselli, Feb 08 2012