|
%I #17 Apr 16 2023 20:34:42
%S 0,1,437,32338,898774,13420861,130567049,929084572,5210829060,
%T 24240197433,96985597357,342789175982,1092151142842,3186269918917,
%U 8618003504977,21826239750488,52182586901800
%N Polynexus numbers of order 15.
%H Bruno Berselli, <a href="/A088893/b088893.txt">Table of n, a(n) for n = 1..1000</a>
%H X. Acloque, <a href="http://www.fortunecity.fr/polynexus/index.html">Polynexus Numbers and other mathematical wonders</a> [broken link]
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
%F 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).
%F 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
%t Table[((n^15 - (n - 1)^15) - (n^3 - (n - 1)^3))/32760, {n, 20}] (* _Bruno Berselli_, Feb 08 2012 *)
%Y Cf. A079547, A083200, A088889, A088890, A088891, A088892, A088894.
%K nonn,easy
%O 1,3
%A Xavier Acloque, Oct 21 2003
%E First term added according to the formula from Bruno Berselli, Feb 08 2012
|
