A088891 Polynexus numbers of order 9.
0, 1, 38, 481, 3355, 16120, 60071, 186238, 502386, 1215435, 2694340, 5559191, 10803013, 19953466, 35282365, 60071660, 98945236, 158276613, 246683346, 375619645, 560079455, 819422956, 1178340163, 1667966026, 2327162150, 3203980975, 4357328976, 5858846163
Offset: 1
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 (9,-36,84,-126,126,-84,36,-9,1).
Programs
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Mathematica
Table[((n^9-(n-1)^9)-(n^3-(n-1)^3))/504,{n,30}] (* or *) LinearRecurrence[ {9,-36,84,-126,126,-84,36,-9,1},{0,1,38,481,3355,16120,60071,186238,502386},30] (* Harvey P. Dale, Jan 18 2012 *)
Formula
a(n) = ((n^9-(n-1)^9)-(n^3-(n-1)^3))/504 = ((n^9-(n-1)^9)-(n^3-(n-1)^3))/(2^9-2^3).
a(1)=1, a(2)=38, a(3)=481, a(4)=3355, a(5)=16120, a(6)=60071, a(7)=186238, a(8)=502386, a(9)=1215435, a(n)=9*a(n-1)-36*a(n-2)+ 84*a(n-3)- 126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Jan 18 2012
G.f.: x^2*(1+29*x+175*x^2+310*x^3+175*x^4+29*x^5+x^6)/(1-x)^9. - Bruno Berselli, Feb 10 2012
Extensions
Offset changed and first term added (according to the formula) from Bruno Berselli, Feb 08 2012