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 A101091 Fourth partial sums of fourth powers (A000583). 10
 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; text; internal format)
 OFFSET 1,2 LINKS Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1). 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). [Harvey P. Dale, Dec 30 2011] G.f.: x*(1+x)*(1+10*x+x^2)/(1-x)^9. [Colin Barker, Apr 04 2012] 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] (* Harvey P. Dale, Dec 30 2011 *) CROSSREFS Cf. A101090. Sequence in context: A164605 A000492 A015866 * A120693 A120692 A324948 Adjacent sequences:  A101088 A101089 A101090 * A101092 A101093 A101094 KEYWORD easy,nonn AUTHOR Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 14 2004 EXTENSIONS Edited by Ralf Stephan, Dec 16 2004 STATUS approved

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Last modified September 19 23:59 EDT 2019. Contains 327207 sequences. (Running on oeis4.)