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A088891
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Polynexus numbers of order 9.
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6
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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; internal format)
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OFFSET
| 1,3
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LINKS
| Bruno Berselli, Table of n, a(n) for n = 1..1000
X. Acloque, Polynexus Numbers and other mathematical wonders [broken link]
Index to sequences with linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
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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
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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] (* From Harvey P. Dale, Jan 18 2012 *)
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CROSSREFS
| Cf. A079547, A083200, A088889, A088890, A088892, A088893, A088894.
Sequence in context: A039685 A006418 A160317 * A159784 A202715 A094034
Adjacent sequences: A088888 A088889 A088890 * A088892 A088893 A088894
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Xavier Acloque, Oct 21 2003
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EXTENSIONS
| Offset changed and first term added (according to the formula) from Bruno Berselli, Feb 08 2012
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