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A088891 Polynexus numbers of order 9. 6
0, 1, 38, 481, 3355, 16120, 60071, 186238, 502386, 1215435, 2694340, 5559191, 10803013, 19953466, 35282365, 60071660, 98945236, 158276613, 246683346, 375619645, 560079455, 819422956, 1178340163 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 26 13:53 EDT 2022. Contains 354883 sequences. (Running on oeis4.)