A088893 Polynexus numbers of order 15.

0, 1, 437, 32338, 898774, 13420861, 130567049, 929084572, 5210829060, 24240197433, 96985597357, 342789175982, 1092151142842, 3186269918917, 8618003504977, 21826239750488, 52182586901800, 118565859736497, 257462955231909, 536839834252906, 1079191653936254

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 (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Crossrefs

Cf. A079547, A083200, A088889, A088890, A088891, A088892, A088894.

Programs

Mathematica

Table[((n^15 - (n - 1)^15) - (n^3 - (n - 1)^3))/32760, {n, 20}] (* Bruno Berselli, Feb 08 2012 *)

Formula

a(n) = ((n^15-(n-1)^15)-(n^3-(n-1)^3))/32760 = ((n^15-(n-1)^15)-(n^3-(n-1)^3))/(2^15-2^3).

G.f.: x^2*(1+422*x+25888*x^2+459134*x^3+3137271*x^4+9505116*x^5+13661136*x^6+9505116*x^7+3137271*x^8+459134*x^9+25888*x^10+422*x^11+x^12)/(1-x)^15. - Bruno Berselli, Feb 08 2012

Extensions

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