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 A254642 Third partial sums of eighth powers (A001016). 6
 1, 259, 7335, 86765, 629174, 3314178, 13906578, 49183590, 152191935, 422931613, 1075761505, 2540663307, 5633367740, 11829663860, 23692442292, 45516670332, 84278105421, 150996708135, 262656041515, 444856105561, 735419759634, 1189222877270 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Luciano Ancora, Table of n, a(n) for n = 1..1000 Luciano Ancora, Partial sums of m-th powers with Faulhaber polynomials Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1). FORMULA G.f.: (x + 247*x^2 + 4293*x^3 + 15619*x^4 + 15619*x^5 + 4293*x^6 + 247*x^7 + x^8)/(- 1 + x)^12. a(n) = n*(1 + n)*(2 + n)*(3 + n)*(3 + 2*n)*(1 + 36*n - 69*n^2 + 45*n^4 + 18*n^5 + 2*n^6)/3960. a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + n^8. EXAMPLE First differences:   1, 255, 6305, 58975, 325089, ...(A022524) -------------------------------------------------------------------- The eighth powers:   1, 256, 6561, 65536, 390625, ...(A001016) -------------------------------------------------------------------- First partial sums:  1, 257, 6818, 72354, 462979, ...(A000542) Second partial sums: 1, 258, 7076, 79430, 542409, ...(A253636) Third partial sums:  1, 259, 7335, 86765, 629174, ...(this sequence) MATHEMATICA Table[n (1 + n) (2 + n) (3 + n) (3 + 2 n) (1 + 36 n - 69 n^2 + 45 n^4 + 18 n^5 + 2 n^6)/3960, {n, 22}] Accumulate[Accumulate[Accumulate[Range[22]^8]]] CoefficientList[Series[(1 + 247 x + 4293 x^2 + 15619 x^3 + 15619 x^4 + 4293 x^5 + 247 x^6 + x^7)/(- 1 + x)^12, {x, 0, 22}], x] PROG (PARI) a(n)=n*(1+n)*(2+n)*(3+n)*(3+2*n)*(1+36*n-69*n^2+45*n^4+18*n^5+2*n^6)/3960 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A000542, A001016, A022524, A253636. Sequence in context: A082788 A043376 A038480 * A322882 A256594 A229433 Adjacent sequences:  A254639 A254640 A254641 * A254643 A254644 A254645 KEYWORD nonn,easy AUTHOR Luciano Ancora, Feb 05 2015 STATUS approved

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Last modified May 20 02:22 EDT 2019. Contains 323411 sequences. (Running on oeis4.)