A088894 Polynexus numbers of order 16.

0, 1, 656, 64895, 2263323, 40728358, 464160877, 3788798018, 23985732786, 124343403711, 548683300726, 2120490369833, 7334132330405, 23085114905772, 67009386720139, 181293280189204, 461148470725844, 1110780513139917, 2548868780082828, 5600100525524707

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 (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Crossrefs

Cf. A079547, A083200, A088889, A088890, A088891, A088892, A088893.

Programs

Mathematica

Table[((n^16 - (n - 1)^16) - (n^4 - (n - 1)^4))/65520, {n, 20}] (* Bruno Berselli, Feb 08 2012 *)

Formula

a(n) = ((n^16-(n-1)^16)-(n^4-(n-1)^4))/65520 = ((n^16-(n-1)^16)-(n^4-(n-1)^4))/(2^16-2^4).

G.f.: x^2*(1+x)*(1+639*x+53880*x^2+1249283*x^3+10687767*x^4+38266494*x^5+59151072*x^6+38266494*x^7+10687767*x^8+1249283*x^9+53880*x^10+639*x^11+x^12)/(1-x)^16. - Bruno Berselli, Feb 08 2012

Extensions

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