A088890 Polynexus numbers of order 8.

0, 1, 25, 234, 1290, 5115, 16211, 43700, 104244, 226005, 453805, 855646, 1530750, 2619279, 4313895, 6873320, 10638056, 16048425, 23665089, 34192210, 48503410, 67670691, 92996475, 126048924, 168700700, 223171325, 292073301, 378462150, 485890534, 618466615

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 (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A079547, A083200, A088889, A088891, A088892, A088893, A088894.

Programs

Mathematica

Table[((n^8 - (n - 1)^8) - (n^2 - (n - 1)^2))/252, {n, 26}] (* Bruno Berselli, Feb 10 2012 *)
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,1,25,234,1290,5115,16211,43700},30] (* Harvey P. Dale, Nov 24 2019 *)

Formula

a(n) = ((n^8-(n-1)^8)-(n^2-(n-1)^2))/252 = ((n^8-(n-1)^8)-(n^2-(n-1)^2))/(2^8-2^2).

G.f.: x^2*(1+x)*(1+16*x+46*x^2+16*x^3+x^4)/(1-x)^8. - Bruno Berselli, Feb 10 2012

Extensions

First term added according to the formula from Bruno Berselli, Feb 10 2012