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

1,3

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

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

Mathematica

Table[((n^16 - (n - 1)^16) - (n^4 - (n - 1)^4))/65520, {n, 20}] (* Bruno Berselli, Feb 08 2012 *)
LinearRecurrence[{16, -120, 560, -1820, 4368, -8008, 11440, -12870, 11440, -8008, 4368, -1820, 560, -120, 16, -1}, {0, 1, 656, 64895, 2263323, 40728358, 464160877, 3788798018, 23985732786, 124343403711, 548683300726, 2120490369833, 7334132330405, 23085114905772, 67009386720139, 181293280189204}, 20] (* Harvey P. Dale, Sep 15 2025 *)

Crossrefs

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

Sequence in context: A252679 A252680 A233898 * A015277 A135418 A309963

Adjacent sequences: A088891 A088892 A088893 * A088895 A088896 A088897

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