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A253713 Second partial sums of 13th powers (A010801). 1
1, 8194, 1610710, 70322090, 1359736595, 15709845116, 126948964044, 787943896860, 3990804658005, 17193665419150, 64919238324226, 219638016608374, 677231901484775, 1928540559615320, 5126044286105240, 12827147639965656, 30432829026732009, 68861475279169530, 149343104993864110, 311744734708558690, 628618742162372731 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The formula for the second partial sums of m-th powers is: b(n,m) = (n+1)*F(m) - F(m+1), where F(m) are the m-th Faulhaber's formulas.
LINKS
FORMULA
a(n) = n*(n+1)*(n+2)*(6*n^12+72*n^11+297*n^10+330*n^9-765*n^8-1368*n^7+2059*n^6+2994*n^5-4091*n^4-2724*n^3+4069*n^2+66*n-735)/1260.
a(n) = 2*a(n-1)-a(n-2)+n^13.
MATHEMATICA
Table[n (n+1) (n+2) (6 n^12 + 72 n^11 + 297 n^10 + 330 n^9 - 765 n^8 - 1368 n^7 + 2059 n^6 + 2994 n^5 - 4091 n^4 -2724 n^3 + 4069 n^2 + 66 n - 735) / 1260, {n, 40}] (* Vincenzo Librandi, Jan 19 2015 *)
Nest[Accumulate, Range[30]^13, 2] (* Harvey P. Dale, Jul 24 2018 *)
PROG
(Magma) [n*(n+1)*(n+2)*(6*n^12+72*n^11+297*n^10+330*n^9-765*n^8-1368*n^7+2059*n^6+2994*n^5-4091*n^4-2724*n^3+4069*n^2+66*n-735)/1260: n in [1..30]]; // Vincenzo Librandi, Jan 19 2015
CROSSREFS
Sequence in context: A181134 A345635 A346348 * A168346 A331357 A045060
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Jan 12 2015
STATUS
approved

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Last modified July 5 19:07 EDT 2024. Contains 374028 sequences. (Running on oeis4.)