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A101091
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Fourth partial sums of fourth powers (A000583).
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2
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1, 20, 155, 760, 2814, 8592, 22770, 54120, 117975, 239668, 459173, 837200, 1463020, 2464320, 4019412, 6372144, 9849885, 14884980, 22040095, 32037896, 45795530, 64464400, 89475750, 122592600, 165968595, 222214356, 294471945, 386498080
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.
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FORMULA
| a(n) = {(n*(1 + n)*(2 + n)^2*(3 + n)*(4 + n)*(-1 + 3*n*(4 + n)))/5040}.
a(1)=1, a(2)=20, a(3)=155, a(4)=760, a(5)=2814, a(6)=8592, a(7)=22770, a(8)=54120, a(9)=117975, 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) [From Harvey P. Dale, Dec 30 2011]
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MATHEMATICA
| Nest[Accumulate, Range[30]^4, 4] (* or *) LinearRecurrence[ {9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 20, 155, 760, 2814, 8592, 22770, 54120, 117975}, 30] (* From Harvey P. Dale, Dec 30 2011 *)
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CROSSREFS
| Cf. A101090.
Sequence in context: A164605 A000492 A015866 * A120693 A120692 A159470
Adjacent sequences: A101088 A101089 A101090 * A101092 A101093 A101094
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KEYWORD
| easy,nonn
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AUTHOR
| Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 14 2004
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EXTENSIONS
| Edited by Ralf Stephan, Dec 16 2004
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