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

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 (9,-36,84,-126,126,-84,36,-9,1).

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

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 *)

Crossrefs

Cf. A079547, A083200, A088889, A088890, A088892, A088893, A088894.

Sequence in context: A039685 A006418 A160317 * A159784 A243820 A268765

Adjacent sequences: A088888 A088889 A088890 * A088892 A088893 A088894

Keyword

nonn,easy

Author

Xavier Acloque, Oct 21 2003

Extensions

Offset changed and first term added (according to the formula) from Bruno Berselli, Feb 08 2012

Status

approved